Carbon fiber-reinforced polymer (CFRP) composite is subject to external loads during service life, suffering the interfacial creep between the fiber and the matrix and eventually the interfacial slippage. CFRP composite loses the interfacial integrity due to the interfacial creep and the long-term durability is weakened. In order to understand the degradation, microscopic details of interfacial structural changes during the creep are essential. This study aims to investigate microscopic creep behavior of a carbon fiber/epoxy interface at different shear load levels using molecular dynamics simulations. A molecular interface model consisting of an epoxy molecule bonded to graphite sheets representing the fiber outer layer is constructed, which is validated by comparing the mass density, glass-transition temperature and Young’s modulus of bonded epoxy with experimental measurements. According to the creep simulation, there is a threshold stress for the onset of creep failure, above which the interface detaches. Comparatively, no interfacial detachment occurs under the low stress regime, where the displacement–force curve is plotted and used to quantify the energy barrier to the onset of creep failure. Meanwhile, the strain and stress evolution of the interface are correlated to interfacial structural changes to understand the interfacial creep mechanism. This study provides molecular insights into the interfacial creep behavior in the fiber/matrix system and form the basis of multiscale investigation framework on the interfacial creep behavior.