In a slew of moves, the Browns also placed defensive lineman Emmanuel Stephens on injured reserve and signed free agent long snapper Christian Yount to replace Pontbriand.
Fujita, in his 10th NFL season, started the first 10 games this year for Cleveland and had 51 tackles and one interception. Stephens played all 11 games, starting three, and had 17 tackles.
Pontbriand, who has played all nine of his NFL seasons with the Browns, was waived two days after his bad snap led to Phil Dawson missing a 55-yard field goal late in Sunday's game in Cincinnati.
Mike Nugent kicked a 26-yarder at the other end to win the game for the Bengals.
His replacement, Yount, played seven games for Tampa Bay this season.
The Browns also promoted linebacker Benjamin Jacobs and defensive lineman Brian Sanford to the active roster from the practice squad. They signed defensive lineman Ayanga Okpokowuruk, defensive back David Sims and linebacker Brian Smith to the practice squad.