A method includes monitoring client requests to access software container instances hosted by container host devices of a geographically-distributed software container platform and identifying, for a given software container instance hosted by a first one of the container host devices, geographic clusters of the client requests. The method also includes calculating a network distance from a given one of the geographic clusters to each of at least a subset of the container host devices. The method further includes replicating the given software container instance in a second one of the container host devices responsive to determining that the calculated network distance from the given geographic cluster to the second container host device is at least a threshold amount less than the calculated network distance from the given geographic cluster to the first container host device.