This is a randomized (individuals assigned to study treatment by chance), double blind (neither physician nor participant knows the treatment that the participant receives), 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 to compare the efficacy and safety of ibrutinib given in combination with bendamustine and rituximab (BR) with BR alone in participants newly diagnosed with mantle cell lymphoma (MCL) who are 65 years of age or older. Approximately 520 participants will be randomly assigned in a 1:1 ratio and stratified by simplified Mantle Cell Lymphoma International Prognostic Index (MIPI) score (low risk \[0-3\] versus intermediate risk \[4-5\] versus high risk \[6-11\]). The treatment phase will extend from randomization until discontinuation of all study treatment or the clinical cutoff for the end of study. A cycle is defined as 28 days. All participants will receive open-label (identity of assigned study drug will be known) BR background therapy for a maximum of 6 cycles; participants with a complete response or partial response will continue to receive open-label background therapy with rituximab maintenance every second cycle for a maximum of 12 additional doses. In addition to the background therapy, all participants will receive blinded study drug (ibrutinib or placebo). Participants randomized to treatment Arm A will receive placebo capsules and participants randomized to treatment Arm B will receive ibrutinib capsules. Study drug will be administered daily and continuously until disease progression, unacceptable toxicity, or study end. Participants with stable disease after initial chemoimmunotherapy (BR+ibrutinib/placebo) should continue treatment with ibrutinib/placebo until disease progression, unacceptable toxicity, or study end. Participants with progressive disease must discontinue all study treatment. For participants who discontinue background therapy and do not have progressive disease, treatment with study drug will continue until disease progression or unacceptable toxicity or the clinical cutoff for the final analysis of progression-free survival (PFS). Participants receiving BR, rituximab, or ibrutinib at the clinical cutoff for the final analysis of PFS will continue open-label treatment until disease progression or unacceptable toxicity. Placebo will be stopped when the study is unblinded for the clinical cutoff for the final analysis of PFS. The posttreatment follow-up phase will begin once a participant discontinues bendamustine and rituximab and study drug. Participants who discontinue for reasons other than disease progression must continue to have disease evaluations as outlined in the protocol. Participants who discontinue due to disease progression will be followed for survival and subsequent anti-MCL therapy. The posttreatment follow-up phase will continue until death, lost to follow up, consent withdrawal, or study end, whichever occurs first. Four clinical cutoffs are planned. The first 3 clinical cutoffs will occur when approximately 134, 180, and 265 PFS events have been observed, respectively. The interim analyses and the final analysis of PFS will take place at these 3 clinical cutoffs, respectively; participant treatment assignment will be unblinded and placebo treatment will be stopped at the clinical cutoff for the final analysis of PFS. Treatment unblinding and stopping of placebo treatment could occur before the planned final analysis of PFS if recommended by the independent Data Monitoring Committee (DMC) after an interim analysis. The last cutoff will occur at the end of study, when 60% of the randomized participants have died or the Sponsor terminates the study, whichever comes first. Efficacy assessments will be conducted in accordance with the Revised Response Criteria for Malignant Lymphoma. Safety will be monitored throughout the study and summarized. Blood samples will be drawn for assessment of pharmacokinetic parameters. Blood and bone marrow will be collected for assessment of minimal residual disease and biomarker studies.