The effect of pressure on the optical-absorption edge of Cd In2 S4, Mg In2 S4, and Mn In2 S4 thiospinels at room temperature is investigated up to 20 GPa. The pressure dependence of their band gaps has been analyzed using Urbach's rule. We have found that, within the pressure range of stability of the low-pressure spinel phase, the band gaps of Cd In2 S4 and Mg In2 S4 exhibit a linear blueshift with pressure, whereas the band gap of Mn In2 S4 exhibits a pronounced nonlinear shift. In addition, an abrupt decrease of the band-gap energies occurs in the three compounds at pressures of 10, 8.5, and 7.2 GPa, respectively. Beyond these pressures, the optical-absorption edge redshifts upon compression for the three studied thiospinels. All these results are discussed in terms of the electronic structure of each compound and their reported structural changes.