A collimator module is disclosed for the modular assembly of a collimator for a radiation detector with a multiplicity of absorber elements, which are arranged one behind the other in a collimation direction and held by a carrier. In at least one embodiment, the carrier has at least one alignment device for aligning the collimator module in the collimation direction, which alignment device(s) interact with positioning device(s) in a detector mechanism of the radiation detector when they are integrated into the radiation detector. This provides the preconditions for integrating the collimator module in a fashion that is decoupled from a radiation convertor, and so this allows easy assembly of a collimator and adjustment to a position assumed between a radiation convertor and the collimator. Moreover, a radiation detector with such a collimator module is disclosed.