We estimate the velocity field in a large set of $N$-body simulations including massive neutrino particles, and measure the auto-power spectrum of the velocity divergence field as well as the cross-power spectrum between the cold dark matter density and the velocity divergence. We perform these measurements at four different redshifts and within four different cosmological scenarios, covering a wide range in neutrino masses. We find that the nonlinear correction to the velocity power spectra largely depend on the degree of nonlinear evolution with no specific dependence on the value of neutrino mass. We provide a fitting formula, based on the value of the r.m.s. of the matter fluctuations in spheres of $8h^{-1}$Mpc, describing the nonlinear corrections with 3% accuracy on scales below $k=0.7; h$ Mpc$^{-1}$.
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