Land ice discharge from the Antarctic continent into the ocean is restrained by ice shelves, floating extensions of grounded ice that buttress the glacier outflow. The ongoing thinning of these ice shelves – largely due to enhanced melting at their base in response to global warming – is known to accelerate the release of glacier meltwater into the world oceans, augmenting global sea level. Mechanisms of ocean heat intrusion under the ice base are therefore crucial to project the future of Antarctic ice shelves. Furthermore, ice shelves are weakened by the presence of kilometer-wide full-thickness ice rifts, which are observed all around Antarctica. However, their impact on ocean circulation around and below ice shelves has been largely unexplored as ocean models are commonly characterized by resolutions that are too coarse to resolve their presence. Here, we apply the Massachusetts Institute of Technology general circulation model at high resolution to investigate the sensitivity of sub-shelf ocean dynamics and ice-shelf melting to the presence of a kilometer-wide rift in proximity of the ice front. We find that (a) the rift curtails water and heat intrusion beneath the ice-shelf base and (b) the basal melting of a rifted ice shelf is on average 20 % lower than for an intact ice shelf under identical forcing. Notably, we calculate a significant reduction in melting rates of up to 30 % near the grounding line of a rifted ice shelf. We therefore posit that rifts and their impact on the sub-shelf dynamics are important to consider in order to accurately reproduce and project pathways of heat intrusion into the ice-shelf cavity.