Magnetism provides a fertile platform for discovering emergent quantum phenomena governed by symmetry. Recent developments of spin-space-group (SSG) theory have revealed altermagnets as a distinct class of nonrelativistic collinear magnets with unconventional spin-dependent electronic structures. Here, we demonstrate that altermagnetic symmetry imposes fundamentally different constraints on electronic and excitonic excitations. Although the quasiparticle and two-body Hamiltonians possess identical SSG symmetries, we find that symmetry-protected degeneracies present in the electronic band structure can be intrinsically lifted in the exciton spectrum at specific momenta. This splitting arises solely from the many-body nature of excitons and does not require spin-orbit coupling or noncollinear magnetic order. Combining symmetry analysis with many-body perturbation theory, we predict a novel class of spin-split excitonic quasiparticles, termed alter-excitons, and reveal their characteristic dispersions in altermagnetic systems. Our results establish excitons as a sensitive probe of hidden spin-space symmetries and uncover a new route toward symmetry-engineered many-body phenomena in collinear magnets.