Massive black hole binaries are expected to provide the strongest gravitational wave signals for the Laser Interferometer Space Antenna (LISA), a space mission targeting $\sim \mathrm{mHz}$ frequencies. As a result of the technological challenges inherent in the mission’s design, implementation, and long duration (4 yr nominal), the LISA data stream is expected to be affected by relatively long gaps where no data is collected (either because of hardware failures, or because of scheduled maintenance operations, such as repointing of the antennas toward the Earth). Depending on their mass, massive black hole binary signals may range from quasitransient to very long lived, and it is unclear how data gaps will impact detection and parameter estimation of these sources. Here, we will explore this question by using state-of-the-art astrophysical models for the population of massive black hole binaries. We will investigate the potential detectability of massive black hole binary signals by observing the effect of gaps on their signal-to-noise ratios. We will also assess the effect of the gaps on parameter estimation for these sources, using the Fisher information matrix formalism as well as full Bayesian analyses. Overall, we find that the effect of data gaps due to regular maintenance of the spacecraft is negligible, except for systems that coalesce within such a gap. The effect of unscheduled gaps, however, will probably be more significant than that of scheduled ones.