We describe a procedure to compute a projection of $w \in ℝ^n$ into the intersection of the so-called zero-norm ball $k B_0$ of radius $k$, i.e., the set of $k$-sparse vectors, with a box centered at a point of $k B_0$. The need for such projection arises in the context of certain trust-region methods for nonsmooth regularized optimization. Although the set into which we wish to project is nonconvex, we show that a solution may be found in $O(n \log(n))$ operations. We describe our Julia implementation and illustrate our procedure in the context of two trust-region methods for nonsmooth regularized optimization.