We propose a model, for the first time, to quantitatively estimate the intercore spontaneous Raman scattering (ICSRS) in multicore fiber (MCF) based on the characterization of intercore crosstalk (ICXT). Also, we show the propertis of ICSRS through numerical simulations. Then the impact of ICSRS on quantum key distribution (QKD) is evaluated. It is revealed that both the forward-ICSRS and backward-ICSRS will reduce the maximum transmisson distance and the forward-ICSRS will reduce more. However, over the range of metropolitan area networks, quantum signals are affected only when the powers of classical signals are very high in dense wavelength division multiplexing system. Finally, the spontaneous Raman scattering (SRS) generated in single core fiber and the ICSRS generated in MCF are compared. The power variety trend with the transmission distance of SRS is similar to that of ICSRS, though there are subtle differences.