The authors discuss the Morrey-Herz space boundedness of the commutator \(U_\psi^b\) of the function multiplier \(M_b\) and the weighted Hardy operator \(U_\psi\) defined by \(U_\psi f(x)=\int_{0}^{1}f(tx)\psi(t)\,dt\) \((x\in \mathbb R^n)\), where \(\psi:[0,1)\to[0,\infty)\). When \(\psi\equiv 1\) and \(n=1\), this reduces to the classical Hardy operator \(U: Uf(x)=x^{-1}\int_{0}^{x}f(t)\,dt\). They show that when \(-\infty<\alpha<\infty\), \(\lambda\geq0\), \(0