The club earlier assigned center William Karlsson to its American Hockey League affiliate in Springfield, Massachusetts.
Calvert has 10 goals and nine assists in 49 games this season. The Brandon, Manitoba, native was Columbus' fifth pick, 127th overall, in the 2008 draft and has 39 goals and 43 assists in 202 career NHL games.
Karlsson was acquired on March 2 by Columbus with left wing Rene Bourque and a second-round pick in the 2015 draft from Anaheim in exchange for defenseman James Wisniewski and a 2015 third-round pick. He had a goal and an assist in three games with the Blue Jackets.