We have investigated the electronic states of single-crystal CaFe2As2 under hydrostatic pressure using (57)Fe Mössbauer spectroscopy and magnetization measurements. The center shift and the quadrupole splitting were refined from observed (57)Fe Mössbauer spectra using the single-crystalline sample under pressure at room temperature. A discontinuous decrease in the pressure dependence of the refined center shift was observed at 0.33 GPa without any anomaly in the pressure dependence of the refined quadrupole splitting, indicating a purely electronic state change in CaFe2As2 with a tetragonal structure. Such a change is shown to be reflected in the peak-like anomalies observed in the pressure dependences of the magnetic susceptibility at 0.26 GPa above 150 K. Our results reveal that this pressure-induced electronic state change suppresses the tetragonal-to-orthorhombic structural phase transition accompanied by an antiferromagnetic ordering. We further observed superconductivity in CaFe2As2 below ∼ 8 K around 0.33 GPa although our sample was not in a single phase at this pressure. These findings suggest that the electronic state change observed in CaFe2As2 with the tetragonal structure is relevant to the appearance of the pressure-induced superconductivity in AFe2As2.