As the bound state of two oppositely charged particles, excitons emerge from optically excited semiconductors as the electronic analog of a hydrogen atom. In the two-dimensional (2D) case, realized in either quantum well systems or truly 2D materials such as transition metal dichalcogenides, the relative motion of an exciton is described by two quantum numbers: the principal quantum number n, and a quantum number j for the angular momentum along the perpendicular axis. Conservation of angular momentum demands that only the j = 0 states of the excitons are optically active in a system illuminated by plane waves. Here, we consider the case for spatially structured light sources, specifically for twisted light beams with nonzero orbital angular momentum per photon. Under the so-called dipole approximation where the spatial variations of the light source occur on length scales much larger than the size of the semiconductor’s unit cell, we show that the photon (linear and/or angular) momentum is coupled to the center-of-mass (linear and/or angular) momentum of the exciton. Thus our study establishes that the exciton spectrum is independent from the spatial structure of the light source.