Police are investigating the incident captured on video which shows the priest plunging the infant into a font that is too small.
The Christian leader also felt it necessary to remind everyone that "man cannot turn into an animal."
Patriarch Kirill has repeatedly praised Putin, calling his presidency a "miracle of God."
The president observed Epiphany in a freezing lake by a monastery, one of several increasingly prominent displays of religiosity in recent months.
Communism, like Christianity, preaches "freedom, brotherhood, equality," he said.
The Kremlin earlier claimed the person in the backseat of Putin's car was a member of security services.
The offer, extended to "sodomites" and "perverts," seems like a publicity stunt but the channel insist it is "no joke."
It is not the first time Patriarch Kirill, Russia's highest religious authority, has spoken out against same-sex marriage.
Tatarstan's archdiocese is republishing a series of articles on dinosaurs and dragons.
Patriarch Kirill signed a pro-life petition, also calling for the end of "abortive" contraceptives.
The spectacle of a young rebel being arrested for blasphemy is a teaching aid the Kremlin loves to use to get its message across.