A vector bundle endowed with a nonlinear connection $N$ is called a Berwald vector bundle if the local coefficients of the Berwald linear connection defined by $N$ do not depend on the fibre variable $y$. It is proved that if a Berwald vector bundle is compatible with a Finsler metric, then it is metrizable as a Riemannian vector bundle. This generalizes the analogous result of Z. I. Szabó\ [Tensor (N.S.) {\bf 35} (1981), no.~1, 25--39; MR0614132 (82f:53043)] obtained for tangent bundles.