We measure the Brillouin gain spectra in two cores (the central core and one of the outer cores) of a ~3-m-long, silica-based, 7-core multi-core fiber (MCF) with incident light of 1.55 μm wavelength, and investigate the Brillouin frequency shift (BFS) and its dependence on strain and temperature. The BFSs of both the cores are ~10.92 GHz, and the strain- and temperature-dependence coefficients of the BFS in the central core are 484.8 MHz/% and 1.08 MHz/°C, respectively, whereas those in the outer core are 516.9 MHz/% and 1.03 MHz/°C. All of these values are not largely different from those in a silica single-mode fiber, which is expected because the cores are basically composed of the same material (silica). We then analyze the difference in structural deformation between the two cores when strain is applied to the fiber, and show that it does not explain the difference in the BFS dependence of strain in this case. The future prospect on distributed strain and temperature sensing based on Brillouin scattering in MCFs is finally presented.