Approximate scaling laws with respect to the nuclear charge are introduced for the time-dependent Dirac equation describing hydrogenlike ions subject to laser fields within the dipole approximation. In particular, scaling relations with respect to the laser wavelengths and peak intensities are discussed. The validity of the scaling relations is investigated for two-, three-, four-, and five-photon ionization of hydrogenlike ions with nuclear charges ranging from Z=1 to 92 by solving the corresponding time-dependent Dirac equations adopting the properly scaled laser parameters. Good agreement is found and thus the approximate scaling relations are shown to capture the dominant effect of the response of highly charged ions to intense laser fields compared to that of atomic hydrogen. On the other hand, the remaining differences are shown to allow for the identification and quantification of additional, purely relativistic effects in light-matter interaction.