Electronic and magnetic properties of Ga1−xMnxAs, obtained from first-principles calculations employing the hybrid HSE06 functional, are presented for x = 6.25% and 12.5% under pressures ranging from 0 to 15 GPa. In agreement with photoemission experiments at ambient pressure, we find for x = 6.25% that non-hybridized Mn-3d levels and Mn-induced states reside about 5 and 0.4 eV below the Fermi energy, respectively. For elevated pressures, the Mn-3d levels, Mn-induced states, and the Fermi level shift towards higher energies, however, the position of the Mn-induced states relative to the Fermi energy remains constant due to hybridization of the Mn-3d levels with the valence As-4p orbitals. We also evaluate, employing Monte Carlo simulations, the Curie temperature (TC). At zero pressure, we obtain TC = 181 K, whereas the pressure-induced changes in TC are dTC/dp = +4.3 K/GPa for x = 12.5% and an estimated value of dTC/dp ≈ +2.2 K/GPa for x = 6.25% under pressures up to 6 GPa. The determined values of dTC/dp compare favorably with dTC/dp = +(2-3) K/GPa at p ≤ 1.2 GPa found experimentally and estimated within the p-d Zener model for Ga0.93Mn0.07As in the regime where hole localization effects are of minor importance [M. Gryglas-Borysiewicz et al., Phys. Rev. B 82, 153204 (2010)].