Structural, electronic, optic and vibrational properties of Zinc antimonide (ZnSb) monolayers and their functionalized (semi-fluorinated and fully chlorinated) structures are investigated by means of the first-principles calculations. The phonon dispersion curves reveal the presence of imaginary frequencies and thus confirm the dynamical instability of ZnSb monolayer. The calculated electronic band structure corroborates the metallic character with fully-relativistic calculations. Moreover, we analyze the surface functionalization effect on the structural, vibrational, and electronic properties of the pristine ZnSb monolayer. The semi-fluorinated and fully-chlorinated ZnSb monolayers are shown to be dynamically stable in contrast to the ZnSb monolayer. At the same time, semi-fluorination and fully-chlorination of ZnSb monolayer could effectively modulate the metallic electronic properties of pristine ZnSb. In addition, a magnetic metal to a nonmagnetic semiconductor transition with a band gap of 1 eV is achieved via fluorination, whereas a transition to a semiconducting state with 1.4 eV band gap is found via chlorination of the ZnSb monolayer. According to the optical properties analysis, the first absorption peaks of the fluorinated- and chlorinated-ZnSb monolayers along the in-plane polarization are placed in the infrared range of spectrum, while they are in the middle ultraviolet for the out-of-plane polarization. Interestingly, the optically anisotropic behavior of these novel monolayers along the in-plane polarizations is highly desirable for design of polarization-sensitive photodetectors. The results of the calculations clearly proved that the tunable electronic properties of the ZnSb monolayer can be realized by chemical functionalization for application in the next generation nanoelectronic devices.