We study the enhancement of the quantum decay rate out of a metastable state, via tunneling, in presence of an external sinusoidal force. It is shown that the Floquet picture of quantum mechanics, together with the complex scaling method, provides an adequate methodology to describe the periodically driven decay process in a nonperturbative way. In the limiting cases of extremely slow and fast external forces the numerical results are compared with simple semiclassical estimates. The decay near the fundamental resonance assumes a Lorentzian line shape in agreement with recent experiments on Josephson junctions in the deep quantum regime. For small forces the enhancement grows proportional to the square of the forcing strength and saturates above a threshold value. Additionally our results also exhibit secondary resonances: at higher frequency corresponding roughly to a second harmonic induced by the nonlinear potential shape, and at lower frequency, exactly at the half of the first resonance, revealing a two-photon transition.