We show that the quasistatic dipole moment can be induced by a short extreme ultraviolet (XUV) pulse (XUV rectification effect) in atomic gas medium subjected to an intense infrared (IR) field (IR-dressed atoms). The general theory of the XUV rectification effect for a single IR-dressed atom is presented, which explicitly relates IR-modified polarizability of an atomic system in the XUV range with the induced quasistatic dipole moment. We illustrate general properties of the XUV rectification effect in an atomic system within the analytical zero-range potential model by presenting the dependence on the IR-field intensity and the time delay between XUV and IR pulses.