We report an experimental study of the rotovibrational fundamental PQR-band shapes in the IR absorption spectra of HCl dissolved in condensed rare gases in a wide range of temperatures. The effective vibrational frequencies are determined from analysis of the fine rotational structure partially resolved in the band wings. The central Q-branch components appear redshifted with respect to the effective vibrational frequencies, their shifts in different solvents found to match the HCl stretching mode shifts in binary Rg...HCl van der Waals heterodimers. Theoretical quasi-free rotor and modified rotor models are applied to describe evolution of the band profiles at changing thermodynamic conditions. Both models are shown to reproduce equally well the observed spectral density distributions in the band wings. However, the modified rotor formalism that accounts for depopulation of the lower-energy rotational solute states provides better agreement with the experiment in the range of the P- and R-branch maxima. We surmise that the Q branches separated from the measured spectral profiles are formed by transitions between rotationally hindered states of diatomic molecules coupled to the solvent by the local anisotropy of the interaction potential.