• Documented informed consent of the participant and/or legally authorized representative.

‣ Assent, when appropriate, will be obtained per institutional guidelines

• Age: ≥ 18 years

• Eastern Cooperative Oncology Group (ECOG) ≤ 2

• Diagnosis of MCL established by histologic assessment including one of the following:

‣ Immunohistochemistry of the biopsy

⁃ Flow cytometry of the biopsy

• Requiring treatment for MCL, and for which no prior systemic anticancer therapies have been received

‣ Local radiotherapy not exceeding a total dose of 20 gray (Gy) at least 2 weeks prior the first dose of study therapy is allowed

• Laboratory, radiographic, physical exam findings and/or symptoms attributable to MCL.

‣ Asymptomatic patients with blastoid or pleomorphic variant can be enrolled

• Radiographically measurable lymphadenopathy or extranodal lymphoid malignancy (as defined by Lugano Classification for non hodgkin's lymphoma \[NHL\])

• Without bone marrow involvement: absolute neutrophil count (ANC) ≥ 1,000/mm\^3, with bone marrow involvement: ANC ≥ 500/mm\^3

‣ NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement

• Without bone marrow involvement: platelets ≥ 75,000/mm\^3 with bone marrow involvement: platelets ≥ 30,000/mm\^3

‣ NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement

• Total bilirubin ≤ 1.5 × upper limit of normal (ULN) OR direct bilirubin ≤ ULN for participants with total bilirubin levels \> 1.5 × ULN

• Aspartate aminotransferase (AST) ≤ 2.5 x ULN

• Alanine aminotransferase (ALT) ≤ 2.5 x ULN

• Serum creatinine ≤ 1.5 × ULN OR creatinine clearance of ≥ 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula

• If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin time (PT) ≤ 1.5 × ULN, if on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants

• If not receiving anticoagulants: activated partial thromboplastin time (aPTT) ≤ 1.5 × ULN, if on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants

• Seronegative for hepatitis C virus (HCV), hepatitis B virus (HBV) (surface antigen negative) OR

‣ If seropositive for HBV or HCV, nucleic acid quantitation must be performed. Viral load must be undetectable. Patients with occult or prior HBV infection (defined as negative hepatitis B surface antigen \[HBsAg\] and positive hepatitis B core antibody \[HBcAb\]) may be included if HBV deoxyribonucleic acid (DNA) is undetectable, if they are willing to undergo DNA testing on day 1 of every cycle and every three months for at least 12 months after the last cycle of study treatment

• Participants with HIV are eligible if they meet ALL the following:

‣ CD4 count \> 350 cells/uL at screening

⁃ The HIV viral load is below the detectable level as per locally available testing

⁃ Are on a stable antiretroviral therapy (ART) regimen for at least 4 weeks prior to study entry

• NOTE: ART includes drugs, which are NOT strong CYP3A4 inducers (participants receiving ART that are strong CYP3A4 inducers are not eligible to be included in the study).

⁃ HIV screening tests are not required unless:

• Known history of HIV infection

∙ As mandated by local health authority

⁃ Are compliant with their ART NOTE: If the participant has had an AIDS defining opportunistic infection in the past 12 months prior to screening, they are not eligible to be included in the study

• Person of childbearing potential (POCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required

• Participants assigned male sex at birth:

⁃ If capable of producing sperm, the participant agrees to the following during the intervention period and for at least the time needed to eliminate each study intervention after the last dose of study intervention. The length of time required to continue contraception for each study intervention is:

• Nemtabrutinib: 12 days

• Rituximab: 3 months

• Abstains from penile-vaginal intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis) and agrees to remain abstinent OR

• Uses contraception as detailed below unless confirmed to be azoospermic (vasectomized or secondary to medical cause, documented from the site personnel's review of the participant's medical records, medical examination, or medical history interview) as detailed below:

• Uses a penile/external condom plus nonparticipant of childbearing potential who is not currently pregnant and should also be advised of the benefit for that partner to use an additional method of contraception, as a condom may break or leak.

‣ Note: Participants capable of producing ejaculate whose partner is pregnant or breastfeeding must agree to use penile/external condom during each episode of sexual activity in which the partner is at risk of drug exposure via ejaculate.

• Contraceptive use by participants capable of producing sperm should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. If the contraception requirements in the local label for any of the study interventions are more stringent than the requirements above, the local label requirements are to be followed

‣ Participants assigned female sex at birth:

⁃ A participant assigned female sex at birth is eligible to participate if not pregnant or breastfeeding, and at least one of the following conditions applies:

• Is not a person of childbearing potential (POCBP) OR

• Is a POCBP and:

‣ Uses a contraceptive method that is highly effective (with a failure rate of \< 1% per year), with low user dependency, or is abstinent from penile-vaginal intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis), during the intervention period and for at least the time needed to eliminate each study intervention after the last dose of study intervention. The length of time required to continue contraception for each study intervention is:

⁃ Nemtabrutinib: 1 month

⁃ Rituximab: 12 months

⁃ The investigator should evaluate the potential for contraceptive method failure (ie, noncompliance, recently initiated) in relationship to the first dose of study intervention. Contraceptive use by POCBPs should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. If the contraception requirements in the local label for any of the study interventions are more stringent than the requirements above, the local label requirements are to be followed.

• Has a negative highly sensitive pregnancy test (urine or serum) as required by local regulations within 24 hours (for urine test) or 72 hours (for serum test) before the first dose of study intervention. If a urine test cannot be confirmed as negative (e.g., an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive.

• Abstains from breastfeeding during the study intervention period and for at least 30 days after study intervention with nemtabrutinib.

• Medical history, menstrual history, and recent sexual activity has been reviewed by the investigator to decrease the risk for inclusion of a POCBP with an early undetected pregnancy