Abstract We have presented a theoretical study on shallow-donor-related photoionization cross section (PICS) in semiconductors subjected to hydrostatic pressure, magnetic field, and intense laser field within the Vogit configuration. Calculations are performed for the donor ground state using a combination of nonperturbative and variational methods in which intense laser field is exactly taken into account via a laser-dressed Coulomb potential (LdCP). We find that the overall shape of shallow-donor-related PICS depends upon the incident optical field polarization, which is more significant when the incident optical field polarization is parallel to the magnetic field. The donor ground-state binding energy and the optical integrals act in an opposite manner to tailor the magnitudes and peak positions of shallow-donor-related PICS by changing radiation field through the LdCP or by changing magnetic field, hydrostatic pressure, and temperature, leading to a blueshift or redshift of shallow-donor-related PICS spectrum and to a decrease or increase of shallow-donor-related PICS magnitude manipulated by these factors. Thus, we can control the properties of shallow-donor-related PICS with an appropriate choice of two external applied fields, hydrostatic pressure, and temperature to meet some special needs in designing and developing new efficient optoelectronic devices.