Inclusion Criteria:

          -  For Dose-escalation arms (Doses A-D): Have a histologically confirmed
             advanced/metastatic solid tumor and have received, been intolerant to, or been
             ineligible for treatments known to confer clinical benefit.

          -  For Dose Expansion Arm A: Have a histologically confirmed Stage III (unresectable) or
             Stage IV cutaneous melanoma and have received and progressed following 1 or 2 prior
             lines of systemic treatments for metastatic melanoma which must include 1 line of
             treatment with PD-1 or PD-L1 immune checkpoint inhibitor either as monotherapy or in
             combination with other therapy.

          -  For Dose Expansion Arm B: Have a histologically confirmed advanced head and neck
             squamous cell carcinoma (HNSCC) and have received and progressed following 1 or 2
             prior lines of systemic treatments for metastatic HNSCC which must include 1 line of
             treatment with PD-1 or PD-L1 immune checkpoint inhibitor either as monotherapy or in
             combination with other therapy.

          -  For Dose Expansion Arms A and B: Have at least 1 lesion that is amenable to both
             intratumoral (IT) injection and biopsy and have at least 1 distant and/or discrete
             noninjected lesion that is measurable per RECIST 1.1 criteria.

          -  For Dose-escalation Cohorts 2a, 3a, or 4a and Expansion Cohorts (Arms A and B) ONLY:
             Have baseline biopsy performed from 1 of the injectable lesions that are planned for
             IT injection and with tumor tissue provided.

          -  For all arms: Have at least 1 cutaneous or subcutaneous lesion amenable to IT
             injection and must be measurable and meet 1 of the following criteria per Response
             Criteria in Solid Tumors Version 1.1 (RECIST 1.1):

               -  A cutaneous or subcutaneous lesion ≥1 cm in longest diameter for solid tumors, or
                  ≥1.5 cm in short axis for a nodal lesion in participants with solid tumor. The
                  longest diameter for an injectable lesion must be ≤10 cm for both solid tumors
                  and nodal lesions in participants with solid tumors.

               -  Multiple coalescing, superficial lesions that in aggregate have a longest
                  diameter of ≥1 cm and ≤10 cm.

          -  Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG)
             Performance Scale.

          -  Show adequate organ function.

          -  Male participants are eligible to participate if they agree to the following during
             the intervention period and for at least 120 days: either be abstinent from
             heterosexual intercourse as their preferred and usual lifestyle and agree to remain
             abstinent, OR must agree to use contraception unless confirmed to be azoospermic.
             Contraceptive use by men should be consistent with local regulations regarding the
             methods of contraception for those participating in clinical studies.

          -  Female participant is eligible to participate if she is not pregnant or breastfeeding,
             and at least 1 of the following conditions applies:

               -  Is not a woman of childbearing potential (WOCBP)

               -  Is a WOCBP and using a contraceptive method that is highly effective, or be
                  abstinent from heterosexual intercourse as their preferred and usual lifestyle
                  (abstinent on a long term and persistent basis), during the intervention period
                  and for at least 120 days after the last dose of study intervention.

          -  HIV-infected participants must have well controlled HIV on antiretroviral therapy
             (ART), per study criteria.

        Exclusion Criteria:

          -  Has had chemotherapy, definitive radiation, or biological cancer therapy within 4
             weeks (2 weeks for palliative radiation) prior to the first dose of study intervention
             or has not recovered from any adverse events (AEs) that were due to cancer
             therapeutics administered more than 4 weeks earlier. Participants receiving ongoing
             replacement hormone therapy for endocrine immune-related AEs will not be excluded from
             participation in this study.

          -  Has a history of a second malignancy, unless potentially curative treatment has been
             completed with no evidence of malignancy for 2 years. The time requirement does not
             apply to participants who underwent successful definitive resection of basal cell
             carcinoma of the skin, superficial bladder cancer or in situ cervical cancer, or other
             in-situ cancers.

          -  Has clinically active central nervous system metastases and/or carcinomatous
             meningitis.

          -  Has had a severe hypersensitivity reaction to treatment with the monoclonal
             antibody/components of the study intervention or has a history of any contraindication
             or has a severe hypersensitivity to any components of pembrolizumab (≥Grade 3).

          -  Has an active infection requiring therapy.

          -  Has a history of (noninfectious) pneumonitis that required steroids or current
             pneumonitis.

          -  Has an active autoimmune disease that has required systemic treatment in the past 2
             years except vitiligo or resolved childhood asthma/atopy.

          -  Is on chronic systemic steroid therapy in excess of replacement doses (prednisone ≤10
             mg/day is acceptable), or on any other form of immunosuppressive medication.

          -  Participants with known Hepatitis B or C infections or known to be positive for
             hepatitis B antigen/hepatitis B virus DNA or hepatitis C antibody or RNA.

          -  HIV-infected participants with a history of Kaposi's sarcoma and/or Multicentric
             Castleman's Disease.

          -  Has a known psychiatric or substance abuse disorder that would interfere with the
             participant's ability to cooperate with the requirements of the study.

          -  Is pregnant or breastfeeding or expecting to conceive or father children within the
             projected duration of the study, starting with the screening visit through 120 days
             after the last dose of study intervention.

          -  Has not fully recovered from any effects of major surgery without significant
             detectable infection.

          -  Has received a live-virus vaccine within 30 days of planned treatment start.

          -  Is currently participating and receiving study intervention in a study of an
             investigational agent or has participated and received study intervention in a study
             of an investigational agent or has used an investigational device within 28 days of
             administration of V938.

          -  Has a history of re-irradiation for HNSCC at the projected injection site.