The elastic, electronic and optical properties of the ZrS₂ monolayer and the effects of different kinds of in-plane strains on its electronic structure are investigated using first-principles method. By analyzing the strain–energy relationship we show that the ZrS₂ monolayer has a Poisson's ratio of 0.22 and an in-plane stiffness of 75.74 N m⁻¹. The band structures of the ZrS₂ monolayer calculated using both generalized gradient approximation and hybrid functional present an indirect band gap feature. The optical properties of the ZrS₂ monolayer exhibit strong anisotropy. In the low-energy region, the perpendicular dielectric function dominates while in the high-energy range both perpendicular and parallel polarizations contribute. Moreover, strain has significant influence on the band structure. It is found that the band gap of the ZrS₂ monolayer can be continuously modified from zero to 2.47 eV always with an indirect band gap under symmetrical strain in the elastic regime. Remarkably, an indirect-to-direct band gap transition has been observed when the uniaxial strain is applied to the monolayer along either the zigzag or armchair directions.