We control the thickness of GaSe on the level of individual layers and study the corresponding optical absorption via highly sensitive differential transmission measurements. Suppression of excitonic transitions is observed when the number of layers is smaller than a critical value of 8. Through ab-initio modelling we are able to assign this behavior to a fundamental change in the band structure that leads to the formation of a valence band shaped as an inverted Mexican hat in thin GaSe. This intrinsic modulation of the optical properties of GaSe provides attractive resources for the development of functional optoelectronic devices based on a single material.