Recently, the XENON1T experiment has reported an excess in the electronic recoil events. The excess is consistent with the interpretation of absorption of 3 keV bosonic dark matter, for example, hidden photon dark matter with kinetic mixing of the order of 10−15. We point out that the minimally gravitational production provides a viable mechanism for obtaining a correct relic hidden photon abundance. We present parameter dependence of the hidden photon dark matter abundance on the inflationary scale Hinf and also the reheating temperature TR. We show that the inflationary Hubble scale and reheating temperature are both bounded from below, Hinf≳7×1011 GeV,TR≳102 GeV. In particular, the high-scale inflation is consistent with 3 keV hidden photon dark matter.