The influence of an intense laser field on shallow-donor states in cylindrical GaAs–Ga1−xAlxAs quantum-well wires under an external magnetic field applied along the wire axis is theoretically studied. Numerical calculations are performed in the framework of the effective-mass approximation, and the impurity energies corresponding to the ground state and 2p ± excited states are obtained via a variational procedure. The laser-field effects on the shallow-donor states are considered within the extended dressed-atom approach, which allows one to treat the problem 'impurity + heterostructure + laser field + magnetic field' as a renormalized 'impurity + heterostructure + magnetic field' problem, in which the laser effects are taken into account through a renormalization of both the conduction-band effective mass and fundamental semiconductor gap.