This is a randomized (individuals assigned to study treatment by chance), double-blind (individuals and study personnel will not know the identity of study treatments), placebo (an inactive substance that is compared with a drug to test whether the drug has a real effect in a clinical trial)-controlled study in approximately 400 adult participants with follicular lymphoma or marginal zone lymphoma. The study will include the following phases: Screening, Treatment, and a Post-treatment Follow-up. Eligible participants will be randomly assigned in a 1:1 ratio to either treatment Arm A (background immune-chemotherapy + placebo) or treatment Arm B (background immune-chemotherapy + 560 milligram [mg] of ibrutinib). All participants will receive 6 cycles of background immune-chemotherapy with either BR or R-CHOP in combination with either placebo (Arm A) or ibrutinib (Arm B). Selection of background immune-chemotherapy will be based on prior treatment history and cardiac function. After completion of background immune-chemotherapy, study drug (ibrutinib or placebo) will continue until disease progression, unacceptable toxicity, or study end, whichever comes first. Assessment of tumor response and progression will be conducted in accordance with the Revised Response Criteria for Malignant Lymphoma. Serial pharmacokinetic (study of what a drug does to the body) blood samples will be collected. Safety will be assessed throughout the study.