Undrafted, Kalinin played professionally in his native Russia with Kontinental Hockey League club, Avangard Omsk.

On May 29, 2015, Kalinin left Avangard Omsk and signed a one-year entry-level deal with the New Jersey Devils of the NHL.

[4] He cleared the following day, but was traded to the Toronto Maple Leafs in exchange for defensive prospect Viktor Lööv.

After finishing the year with the Marlies, Kalinin as a free agent from the Maple Leafs, chose to return to his native Russia, signing a three-year deal with SKA Saint Petersburg of the KHL on July 1, 2017.

[6] Approaching the 2018–19 season, Kalinin was traded by SKA to fellow powerhouse club, HC CSKA Moscow in exchange for Andrei Kuzmenko on August 8, 2018.