We study correlation functions in a scalar field theory on the fuzzy sphere, which is realized by a matrix model where the matrix size plays a role of the UV cutoff. We identify the Berezin symbol for a matrix with a field, and we calculate the correlation functions of the fields by Monte Carlo simulation. By tuning a parameter of the theory, we find that the two-point and four-point correlation functions agree for different matrix sizes. This result strongly suggests that the theory is renormalizable.