This paper presents a Model Predictive Controller (MPC) that uses navigation integrity risk as a constraint. Navigation integrity risk accounts for the presence of faults in localization sensors and algorithms, an increasingly important consideration as the number of robots operating in life and mission-critical situations is expected to increase dramatically in near future (e.g. a potential influx of self-driving cars). Specifically, the work uses a local nearest neighbor integrity risk evaluation methodology that accounts for data association faults as a constraint in order to guarantee localization safety over a receding horizon. Moreover, state and control-input constraints have also been enforced in this work. The proposed MPC design is tested using real-world mapped environments, showing that a robot is capable of maintaining a predefined minimum level of localization safety while operating in an urban environment.