The author proves a Bogolyubov-type averaging theorem for a differential inclusion \(D_ hX(t)\in\varepsilon F(t,X(t))\), \(X(0)=X^ 0\), where \(D_ hX(t)\) is the Hukuhara derivative of a set-valued map taking values in \(\text{Conv}(\mathbb{R}^ n)\), the space of nonempty compact and convex subsets of \(\mathbb{R}^ n\), and the values of a set-valued map \(F\) are compact subsets of \(\text{Conv}(\mathbb{R}^ n)\). The proof involves the concept of the mixed Aumann-Hukuhara integral of a set-valued map \(F\).