ABSTRACT We test the hypothesis that the observed first-peak (Sr, Y, Zr) and second-peak (Ba) s-process elemental abundances in low-metallicity Milky Way stars, and the abundances of the elements Mo and Ru, can be explained by a pervasive r-process contribution originating in neutrino-driven winds from highly magnetic and rapidly rotating proto-neutron stars (proto-NSs). We construct chemical evolution models that incorporate recent calculations of proto-NS yields in addition to contributions from asymptotic giant branch stars, Type Ia supernovae, and two alternative sets of yields for massive star winds and core-collapse supernovae. For non-rotating massive star yields from either set, models without proto-NS winds underpredict the observed s-process peak abundances by 0.3–$1\, \text{dex}$ at low metallicity, and they severely underpredict Mo and Ru at all metallicities. Models incorporating wind yields from proto-NSs with spin periods P ∼ 2–$5\, \text{ms}$ fit the observed trends for all these elements well. Alternatively, models omitting proto-NS winds but adopting yields of rapidly rotating massive stars, with vrot between 150 and $300\, \text{km}\, \text{s}^{-1}$, can explain the observed abundance levels reasonably well for [Fe/H] < −2. These models overpredict [Sr/Fe] and [Mo/Fe] at higher metallicities, but with a tuned dependence of vrot on stellar metallicity they might achieve an acceptable fit at all [Fe/H]. If many proto-NSs are born with strong magnetic fields and short spin periods, then their neutrino-driven winds provide a natural source for Sr, Y, Zr, Mo, Ru, and Ba in low-metallicity stellar populations. Conversely, spherical winds from unmagnetized proto-NSs overproduce the observed Sr, Y, and Zr abundances by a large factor.