Inclusive doubly differential cross sections d^2\sigma_{pA}/dx_Fdp_T^2 as a function of Feynman-x (x_F) and transverse momentum (p_T) for the production of K^0_s, Lambda^0 and anti-Lambda^0 in proton-nucleus interactions at 920 GeV are presented. The measurements were performed by HERA-B in the negative x_F range (-0.12<x_F<0.0) and for transverse momenta up to p_T= 1.6 GeV/c. Results for three target materials: carbon, titanium and tungsten are given. The ratios of production cross sections are presented and discussed. The Cronin effect is clearly observed for all three V^0 species. The atomic number dependence is parameterized as \sigma_{pA} = \sigma_{pN} \cdot A^\alpha where \sigma_{pN} is the proton-nucleon cross section. The measured values of \alpha are all near one. The results are compared with EPOS 1.67 and PYTHIA 6.3. EPOS reproduces the data to within \approx 20% except at very low transverse momentum.