Inclusion Criteria:

          -  Confirmed diagnosis of MCL with CD20 and cyclin D1 positivity in tissue biopsy.
             Patients must have never received any prior therapy for their disease. Patients have
             been observed for 3 - 6 months with no progression as per imaging assessments

          -  High risk smoldering MCL: non-blastoid variant histology, non-pleomorphic variant
             histology with a Ki-67 of 20-30% and absence of B symptoms with/without white blood
             cell (WBC) 15-30k, lymph nodes =< 5 cm in diameter, non-blastoid/pleomorphic with a
             complex karyotype, TP53 mutated or wild type, del17p (fluorescence in situ
             hybridization [FISH]% 10-50%), MYC positive , presence of NOTCH2, NSD2 or more than
             one mutation in the initial next generation sequencing (NGS) panel testing but who are
             asymptomatic and do not have any clinical indication to start systemic therapy

          -  Understand and voluntarily sign an institutional review board (IRB)-approved informed
             consent form

          -  Patients should in general have bi-dimensional measurable disease with their biggest
             tumor less than or equal to 5 cm. (Bone marrow or gastrointestinal [GI] only
             involvement is acceptable)

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less

          -  With minimal disease related symptoms but anxious to start systemic therapy

          -  Absence of cytopenia attributed to bone marrow (BM) infiltration

          -  Absolute neutrophil count (ANC) > 1000/mm^3

          -  Platelet count > 100,000/mm^3

          -  Patients who have bone marrow infiltration by MCL are eligible if their ANC is >= than
             500 or their platelet level is >= than 50,000 /mm^3. Platelet transfusions are allowed

          -  Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and
             alanine aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) < 3 x upper
             limit of normal or < 5 x upper limit of normal if hepatic metastases are present

          -  Serum bilirubin < 1.5 mg/dl

          -  Creatinine (Cr) clearance >= 30 mL/min

          -  Disease free of prior malignancies of equal to or greater than 6 months with exception
             of currently treated basal cell, squamous cell carcinoma of the skin, carcinoma "in
             situ" of the cervix or breast, or other malignancies in remission (including prostate
             cancer patients in remission from radiation therapy, surgery or brachytherapy), not
             actively being treated. Patients must be willing to receive transfusions of blood
             products

          -  Willing and able to participate in all study related procedures and therapy including
             swallowing capsules without difficulty and having a screening core biopsy

          -  Female subjects who are of non-reproductive potential (i.e., post-menopausal by
             history - no menses for >= 1 year; OR history of hysterectomy; OR history of bilateral
             tubal ligation; OR history of bilateral oophorectomy). Female subjects of childbearing
             potential must have a negative serum pregnancy test upon study entry

          -  Male and female subjects who agree to use highly effective methods of birth control
             (e.g., implants, injectables, combined oral contraceptives, some intrauterine devices
             [IUDs], sexual abstinence, or sterilized partner) and a barrier method (e.g., condoms,
             vaginal ring, sponge, etc) during the period of therapy and for 30 days after the last
             dose of study drug for females and 90 days for males

        Exclusion Criteria:

          -  Any serious medical condition including but not limited to uncontrolled hypertension,
             diabetes mellitus, active/symptomatic coronary artery disease, chronic obstructive
             pulmonary disease (COPD), renal failure, splenomegaly, leukemic features, active
             hemorrhage, or psychiatric illness that, in the investigator's opinion, places the
             patient at unacceptable risk and would prevent the subject from signing the informed
             consent form

          -  Patients with ANY of the following risk factors:

               -  Significant disease related symptoms (including significant B symptoms)

               -  Blastoid variant histology

               -  Pleomorphic variant histology

               -  Ki-67 > 30%

               -  Bulky tumors > 5 cm

               -  Central nervous system (CNS) involvement at diagnosis

          -  All patients must not have received any prior treatment for mantle cell lymphoma

          -  Prior exposure to BTK inhibitor

          -  Pregnant or breastfeeding females

          -  Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus
             (HCV) or hepatitis B virus (HBV). Subjects who are positive for hepatitis B core
             antibody, hepatitis B surface antigen, or hepatitis C antibody must have a negative
             polymerase chain reaction (PCR) result before enrollment. Those who are PCR positive
             will be excluded

          -  All patients with history of central nervous system lymphoma

          -  History of stroke or intracranial hemorrhage within 6 months prior to signing the
             consent

          -  Currently active, clinically significant cardiovascular disease such as uncontrolled
             arrhythmia or any class 3 or 4 congestive heart failure as defined by the New York
             Heart Association Classification, or a history of myocardial infarction, unstable
             angina, or acute coronary syndrome within 6 months prior to randomization

          -  Significant screening electrocardiogram (ECG) abnormalities including left bundle
             branch block, 2nd degree atrioventricular (AV) block type II, 3rd degree block,
             bradycardia (< 50 beats per minute [bpm]), or corrected QT (QTc) > 500 msec

          -  Unable to swallow capsules, malabsorption syndrome, disease significantly affecting
             gastrointestinal function, or resection of the stomach or small bowel or ulcerative
             colitis, symptomatic inflammatory bowel disease, or partial or complete bowel
             obstruction

          -  Requires concomitant anticoagulation with warfarin or equivalent vitamin K antagonist,
             active treatment for pulmonary embolism (PE)/ deep vein thrombosis (DVT) and persons
             with mechanical cardiac valves

          -  Subject who received a strong cytochrome P450 (CYP) 3A inhibitor within 7 days prior
             to the first dose of ibrutinib or subject who requires continuous treatment with a
             strong CYP3A inhibitor

          -  Subjects with chronic liver disease and hepatic impairment meeting Child-Pugh class C

          -  Any uncontrolled active systemic infection

          -  Major surgery within 4 weeks of first dose of study drug

          -  Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug

          -  Recent infection requiring systemic treatment that was completed =< 14 days before the
             first dose of study drug

          -  Known bleeding disorders (e.g., von Willebrand's disease or hemophilia)

          -  Unresolved toxicities from prior anticancer therapy, defined as having not resolved to
             Common Terminology Criteria for Adverse Event (CTCAE, version [v] 4.0), grade =< 1, or
             to the levels dictated in the inclusion/exclusion criteria with the exception of
             alopecia

          -  Concurrent systemic immunosuppressant therapy within 21 days of the first dose of
             study drug