We test the effects of an approximate treatment of two-body contributions to the axial-vector current on the quasiparticle random-phase approximation (QRPA) matrix elements for neutrinoless double-beta decay in a range of isotopes. The form and strength of the two-body terms come from chiral effective-field theory. The two-body currents typically reduce the matrix elements by about 20%, not as much as in shell-model calculations. One reason for the difference is that standard practice in the QRPA is to adjust the strength of the isoscalar pairing interaction to reproduce two-neutrino double-beta decay lifetimes. Another may be the larger QRPA single-particle space. Whatever the reasons, the effects on neutrinoless decay are significantly less than those on two-neutrino decay, both in the shell model and the QRPA.