The 26-year-old was added to the club's roster on emergency recall on March 8.
Drazenovic didn't have a point in seven games with Columbus. He has 16 goals and 30 assists in 47 games with Springfield this season.
He ranks second on the Falcons in assists, points and power-play goals (nine) and is tied for fourth in goals. In 41 games with Springfield last season, Drazenovic had 13 goals and 28 assists.