We give a modular branching rule for certain wreath products as a generalization of Kleshchev's modular branching rule for the symmetric groups. Our result contains a modular branching rule for the complex reflection groups G (m, 1, n), which are often called the generalized symmetric groups, in splitting fields for Z/mZ. Especially for m = 2, which is the case of the Weyl groups of type B, we can give a modular branching rule in any field. (C) 2006 Elsevier Inc. All rights reserved.