Brickley skated just 9:05 in Saturday's season finale against the Penguins, finishing the season with a goal and three assists in 14 appearances.
Brickley was a healthy scratch during Wednesday's 4-1 loss to Vancouver.
Brickley potted a goal in Tuesday's win over the Hurricanes.
Brickley was recalled from AHL Hartford on Thursday.
Nashville traded Brickley to the Rangers on Monday in exchange for Cole Schneider.
Brickley signed a one-year, two-way contract with the Predators on Sunday. The deal is worth $650,000 at the NHL level and $300,000 in the AHL.
Brickley finished with four goals and eight assists over 44 games in 2017-18, while averaging 11:53 of ice time.
Brickley scored the game-winning goal and set up the insurance marker in a 2-0 win over the Canadiens on Saturday night.
Brickley (upper body) will return to the lineup Saturday night against the Rangers.
Coach Bob Boughner says that Brickley (upper-body) is probable to return Saturday against the Rangers, Matthew DeFranks of the Sun-Sentinel reports.