We report the magnetic proximity effect (MPE) and valley non-degeneracy in monolayer MoS2 and magnetic semiconductor EuS thin film heterojunctions studied by density functional theory (DFT) with the vdW-DF2 correlations. Magnetic moments are observed in MoS2 due to the MPE when forming chemical or van der Waals (vdW) adsorption states with EuS. Spin-orbit coupling (SOC) leads to observable valley non-degeneracy of MoS2 at the K (K') points in the Brillouin zone. The valley Zeeman splitting energy Ez can reach 5.1 meV and 37.3 meV for the vdW and chemical adsorption states, corresponding to a magnetic exchange field (MEF) of 22 T and 160 T respectively. By applying a gate voltage across the MoS2/EuS interface, it is found that Ez can be tuned from 1.8 meV to 8.2 meV and from 24.5 meV to 53.8 meV for vdW and chemical adsorption states respectively. The strong MPE, large and tunable valley degeneracy in 2D material and ferromagnetic semiconductor/insulator vdW heterojunctions demonstrate their promising potential for novel optoelectronic and valleytronic device applications.