Distributed Cloud environments are now resorting to Cloud applications composed of heterogeneous microservices. Cloud service providers strive to provide high quality of service (QoS) and response time is one of the key QoS attributes for microservices. The dynamism of microservice ecosystems necessitates runtime adaptations and microservices rescheduling to avoid performance degradation. Existing works target rescheduling in hypervisor‐based systems, while ignoring the influence of configuration parameters of container‐based microservices. In an effort to address these challenges, this article describes a novel microservice rescheduling framework, throttling and interaction‐aware anticorrelated rescheduling for microservices, to proactively perform rescheduling activities whilst ensuring timely service responses. Based on periodic monitoring of the performance attributes, the framework schedules container migrations. Considering the exponentially large solution space, a metaheuristic approach based on multiverse optimization is developed to generate the near‐optimal mapping of microservices to the datacenter resources. Experimental results indicate that our framework provides superior performance with a reduction of up to 13.97% in the average response time, when compared with systems with no support for rescheduling.