The different mechanisms that contribute to the renormalization of the effective induced pseudoscalar coupling constant in nuclei are described. For a nucleon in the nuclear medium one has to consider four different induced pseudoscalar couplings, which are associated with the space- and time-like parts of the current and the pseudovector source function, respectively. All of these are renormalized in different ways in the medium. The net effect for weak processes with large time-like momentum transfer is a substantial quenching of the transition rates that increases with mass number in agreement with recent data on radiative muon capture on heavy nuclei.