Interface diffusion is an important weakening mechanism in the creep behavior of metal matrix composites at high temperatures. The increase in the creep strength of composite materials caused by stress transfer from matrix to rigid reinforcements may be totally offset by rapid interface diffusion. However, in-depth understanding of the complex multi-field coupling process of interface diffusion remains lacking. Here, we present a theoretical method in the framework of micromechanics theory based on Eshelby's solution to solve this problem. The misfit deformation and stress redistribution caused by mass diffusion are taken into account by introducing a time-evolving eigenstrain into reinforcements. Mass conservation in the diffusion process, is guaranteed by keeping the volume constant, leading to incompressibility of creep strains. In this work, the creep behavior of composites induced by interface diffusion is systematically studied, including macroscopic creep strain and stress relaxation. Closed-form solutions are obtained and verified by finite element simulation with a built-in time-step algorithm. This methodology can be conveniently applied to account for plasticity and creep of matrix, interface debonding, microcracks, etc., paving the way for the study of the complex behavior of composite materials at high temperatures.