  The Minkowski function is a crucial tool used in the study of balanced
domains and, more generally, quasi-balanced domains in several complex
variables. If a quasi-balanced domain is bounded and pseudoconvex then it is
well-known that its Minkowski function is plurisubharmonic. In this short note,
we prove that under the additional assumption of smoothness of the boundary,
the Minkowski function of a quasi-balanced domain is in fact smooth away from
the origin. This allows us to construct a smooth plurisubharmonic defining
function for such domains. Our result is new even in the case of balanced
domains.
