We study the effect of disorder on the excitons in a semiconductor with screened Coulomb interaction. Examples are polymeric semiconductors and/or van der Waals structures. In the screened hydrogenic problem, we consider the disorder phenomenologically using the so-called fractional Scrödinger equation. Our main finding is that joint action of screening and disorder either destroys the exciton (strong screening) or enhances the bounding of electron and hole in an exciton, leading to its collapse in the extreme case. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in the above semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important. Our theoretical results permit one to predict the various excitonic properties in semiconductor samples with different degrees of disorder and Coulomb interaction screenings.