We investigate the structural, mechanical, and electronic properties of the two-dimensional hexagonal structure of group III-VI binary monolayers, MX (M = B, Al, Ga, In and X = O, S, Se, Te) using first-principles calculations based on the density functional theory. The structural optimization calculations and phonon spectrum analysis indicate that all of the 16 possible binary compounds are thermally stable. In-plane stiffness values cover a range depending on the element types and can be as high as that of graphene, while the calculated bending rigidity is found to be an order of magnitude higher than that of graphene. The obtained electronic band structures show that MX monolayers are indirect band-gap semiconductors. The calculated band gaps span a wide optical spectrum from deep ultraviolet to near infrared. The electronic structure of oxides (MO) is different from the rest because of the high electronegativity of oxygen atoms. The dispersions of the electronic band edges and the nature of bonding between atoms can also be correlated with electronegativities of constituent elements. The unique characteristics of group III-VI binary monolayers can be suitable for high-performance device applications in nanoelectronics and optics.