  We consider the matrix regularization of fields on a Riemann surface which
couple to gauge fields with a nonvanishing magnetic flux. We show that such
fields are described as rectangular matrices in the matrix regularization. We
construct the matrix regularization explicitly for the case of the sphere and
torus based on the Berezin-Toeplitz quantization, and also discuss a possible
generalization to cases with higher genera. We also discuss the matrix version
of the Laplacian acting on the rectangular matrices.
