In the paper, a class of Persidskii-type systems with separable nonlinearities and switching is considered. The stability problem is investigated. Sufficient conditions of the asymptotic and practical stability for a given equilibrium position are obtained. The region of attraction of the equilibrium position is estimated. The main goal of the work is to find conditions on the switching law providing the set size of the region of attraction. The direct Lyapunov method and the theory of differential inequalities are used. To improve the results, different inequalities for a chosen Lyapunov function are constructed in different parts of the phase space. Some numerical examples are presented to illustrate the proposed approach.