Colby Cohen was born on April 25, 1989 in Villanova, Pennsylvania. Cohen was selected by the Colorado Avalanche in the second round, 45th overall, in the 2007 NHL Entry Draft.
Upon signing with the Avalanche, Cohen joined the Lake Erie Monsters of the American Hockey League. He would make his NHL debut on November 6, 2010 in a 5-0 win against the Dallas Stars, but would appear in just three games for the Avs before being returned to the AHL.
On November 29, 2010, Cohen was traded to the Boston Bruins in exchange for Matt Hunwick. He was called up the Bruins prior to the 2011 playoffs and would practice with the club throughout their run to the Stanley Cup. He would not qualify to have his name engraved on the trophy, but for his efforts the Bruins did award him a Stanley Cup championship ring.