There is a significant disagreement between the experimental and theoretical plasma Stark shift of the hydrogenlike helium Paschen-α line (λ=468.568nm). Here, it is demonstrated that the controversy can be resolved by accounting for the plasma polarization shift and other related effects arising from the charged plasma particles penetrating the wave-function extent of the bound electron. For experimental verification, a laser-induced helium plasma with n_{e}=1.50×10^{24}m^{-3} and T_{e}=68200K, as independently determined by using the Thomson scattering method, was studied. Excellent agreement is observed between the theoretical and experimental line width and line shift, and more generally, for the entire line shape.