It is scientifically significant to realize monolayer MoS₂-based magnetic semiconductors and to regulate the spin states of MoS₂ for the development and application of two-dimensional (2D) spintronic devices. In this work, we systematically studied the effects of biaxial strain on the electronic structure, magnetic and optical properties of Co doped monolayer MoS₂ (Co_Mo) systems using the first-principles calculations based on density functional theory (DFT). Our results indicate that the electronic structure, magnetic and optical properties of Co_Mo systems are closely related to biaxial strain. First, strain regulates the energy level sequences of Co-d orbitals. The electronic configurations vary with strains as follows: a+a-e₁+e₁-e₂+e₂- for strains between -9% and -6%, a+e₁+a-e₂+e₁-e₂- for -5% to -4%, e₁+e₂+a+a-e₁-e₂- for -3% to 0%, a+e₁+e₂+a-e₁-e₂- for 1% to 6%, and e₁+a+a-e₁-e₂+e₂- for 7% to 9%, respectively. Second, strain influences the occupancy of Co-d orbitals, thereby affecting the magnetic properties. In the strain range of -9%—-6%, the Co_Mo systems exhibit a local magnetic moment of 1.00 μB, and the coupling between such two moments is ferromagnetic (FM). Within the strain range of -5%—9%, the Co_Mo systems produce a magnetic moment of 3.00 μB, and the coupling between the magnetic moments is antiferromagnetic (AFM) in the range of -5%—-4%, translates to FM states in the range of -3%— 6%, and then changes to AFM states within range of 7%—9%. Among them, the FM coupling strength of the Co_Mo system is strongest at 3% strain, which is favorable for achieving a high Curie temperature (T_C) in MoS₂-based magnetic semiconductors. These oscillatory magnetic interactions are attributed to the d-p-d superexchange and d-d direct-exchange mechanisms. Third, tensile strain enhances the optical properties of Co_Mo systems. Compared to undoped MoS₂, the increased complex dielectric function in the low-energy light region enhances the valence electron transition probability and the separation efficiency of photogenerated electron-hole pairs, leading to a significant improvement in photocatalytic performance for the Co_Mo doped systems. Moreover, the impurity energy levels introduced by Co are located in the band-gap, which reduces the energy for valence electrons to transition to empty bands, thereby increasing photon absorption in the visible and infrared regions in Co_Mo doped systems. Meanwhile, the absorption edge undergoes a red shift, and tensile strain further improves the optical performance of the Co doped monolayer MoS₂ systems in the visible and infrared regions. Finally, dynamic stability analysis under strain reveals that Co_Mo systems are unstable as strain in the range of -9%—-4%. Combined with the magnetic, optical properties, and structural stability of Co_Mo systems, the strain should be in the range of 1%—6%. The results presented here provide a novel approach for fabricating MoS₂-based magnetic semiconductors with superior optical properties.