Stochastic resonance (SR) occurs in nonlinear dynamical systems when the response to a weak coherent input is enhanced by the presence of noise. While classical SR presently is an intensely studied phenomenon, the role of quantum fluctuations has only started to be explored. We study SR in the temperature range where quantum tunneling corrections to the classical rate of activation are relevant. For a particle subject to moderate-to-large friction, we show that the semiclassical SR can be enhanced considerably by quantum fluctuations, as compared to the predictions of a classical analysis.