Fast radio bursts (FRBs) are extragalactic radio transients with millisecond duration and brightness temperature. An FRB-associated X-ray burst (XRB) was recently found to arise from the Galactic magnetar SGR J1935+2154. Following the model of Dai, in which an FRB may originate from a magnetar encountering an asteroid, we focus on explaining the spectrum of the XRB associated with FRB 200428 from SGR J1935+2154. Collisions between asteroidal fragments and the magnetar surface produce a fireball, which further expands relativistically. Due to the velocity difference among some shells in the fireball, internal shocks would form far away from the magnetar, and further emit X-ray emission. We propose that the FRB-associated XRB can be produced by synchrotron emission from the internal shocks, and then constrain the physical parameters by the observed XRB spectrum.