Strain is usually unavoidable in the fabrication of devices based on two-dimensional (2D) transition metal chalcogenides (TMDCs). When metals are deposited onto monolayer TMDCs, strain can be induced at metal-TMDC interfaces and evolves with elapsed time. However, the effect of the substrate on the strain evolution at the metal-TMDC interfaces is still unclear, which hinders the development of reliable 2D TMDC-based devices with perfect contacts. In this work, we investigated the evolution of metal-induced local strains for Ag-deposited monolayer MoS2 on three kinds of substrates with different interface interactions, i.e., sapphire, SiO2/Si, and mica. The interface interaction between MoS2 and sapphire is the strongest, while that between MoS2 and mica is the weakest. With the splitting of MoS2 Raman peaks as an indicator of local strain, the evolution behavior of the local strain at the Ag-MoS2 interfaces is found to greatly depend on the interface interactions from the underlying substrates. With elapsed time, the local strain is best preserved on sapphire but relaxed most easily on mica. Density-functional theory calculations show that the adsorption energies at the interfaces are different for MoS2 on different substrates, suggesting that the interface interaction between monolayer MoS2 and the substrates is crucial for the strain evolution. Our work is of benefit for the study of stability and reliability of devices based on TMDCs, particularly for flexible electronic devices.