The calendar put together by an Orthodox news website sees 12 smiling priests in dark robes relaxing with their cats - sitting side-by-side on the sofa, or having the pet sprawled on their chest or draped round their shoulders.
It is the first calendar to depict priests in such a style, said one of the creators, Ksenia Luchenko, a journalist at the Pravmir website who came up with the idea.
She conceded Russia's powerful Church is not usually open to such an informal depiction of its clerics.
Religious-themed calendars usually just depict holy icons.
"It's all their own cats - nothing was staged," Luchenko said of the casting process for the calendar.
"It was whoever had a cat and was ready to pose for a photo."
Nevertheless the cat-owning priests in the charming black- and-white shots by Anna Galperina turned out to be "nice- looking," she added.
The calendar is not officially endorsed by the Russian Orthodox Church.
Senior Church spokesman Vsevolod Chaplin has said it is "not a great sin" but added: "I wouldn't hang such a calendar on my wall," in comments to Russkaya Sluzhba Novostei radio station.
The calendar was even covered by Russian Cosmopolitan magazine.
"Not all priests agreed to do it. Not everyone wants that kind of publicity," Luchenko said.
The calendar called "Pop i Kot" or "Priest and Cat" grew out of a photography book project showing Russian priests in their everyday lives, she said.
"By chance we had a photo of a priest with a cat and I thought: why not do a series?"
It was only after the calendar was completed that the team realised they had a Roman Catholic competitor: an unofficial calendar published in Rome every year featuring handsome priests called the Calendario Romano, she said.