Given a finitely supported refinement mask on $\bZ^s$ with irrational coefficients, in many applications, we need to truncate the irrational coefficients in the refinement mask to rational numbers. This note provides a sharp error estimate in the $L_p\, (1\le p \le \infty)$ norm sense of a multivariate subdivision scheme caused by truncation of an original refinement mask. Examples are provided to illustrate that the estimate in this note is optimal. Finally, we partially extend this estimate to the case when a refinement mask has infinite support.