Few-layer GaSe is one of the latest additions to the family of two-dimensional semiconducting crystals whose properties under strain are still relatively unexplored. Here, we study rippled nanosheets that exhibit a periodic compressive and tensile strain of up to 5%. The strain profile modifies the local optoelectronic properties of the alternating compressive and tensile regions, which translates into a remarkable shift of the optical absorption band-edge of up to 1.2 eV between crests and valleys. Our experimental observations are supported by theoretical results from density functional theory calculations performed for monolayers and multilayers (up to seven layers) under tensile and compressive strain. This large band gap tunability can be explained through a combined analysis of the elastic response of Ga atoms to strain and the symmetry of the wave functions.