Stimulated by the proton radius conundrum, measurements of the Lamb shift in various light muonic atoms are planned at PSI. The aim is to extract the rms charge radius with high precision, limited by the uncertainty in the nuclear polarization corrections. We present an ab initio calculation of the nuclear polarization for μHe+4 leading to an energy correction in the 2S-2P transitions of δpolA=-2.47 meV ±6%. We use two different state-of-the-art nuclear Hamiltonians and utilize the Lorentz integral transform with hyperspherical harmonics expansion as few-body methods. We take into account the leading multipole contributions, plus Coulomb, relativistic, and finite-nucleon-size corrections. Our main source of uncertainty is the nuclear Hamiltonian, which currently limits the attainable accuracy. Our predictions considerably reduce the uncertainty with respect to previous estimates and should be instrumental to the μHe+4 experiment planned for 2013.