We have studied the effects of optical-frequency light on proximitized InAs/Al Josephson junctions based on highly n-doped InAs nanowires at varying incident photon flux and at three different photon wavelengths. The experimentally obtained IV curves were modeled using a resistively shunted junction model which takes scattering at the contact interfaces into account. Despite the fact that the InAs weak link is photosensitive, the Josephson junctions were found to be surprisingly robust, interacting with the incident radiation only through heating, whereas above the critical current our devices showed non-thermal effects resulting from photon exposure. Our work indicates that Josephson junctions based on highly-doped InAs nanowires can be integrated in close proximity to photonic circuits. The results also suggest that such junctions can be used for optical-frequency photon detection through thermal processes by measuring a shift in critical current.