The Bruins traded McQuaid to the Rangers in exchange for Steve Kampfer, a 2019 fourth-round draft pick and a conditional seventh-rounder Tuesday.
McQuaid finished up the 2017-18 regular season with one goal and four points, to go along with 62 PIM in 38 games.
McQuaid, who was forced out Monday's game with an unspecified injury, practiced Tuesday.
McQuaid left Monday's tilt versus Columbus in the third period with an injury, Joe Haggerty of NBC Sports Boston reports.
McQuaid registered 12 penalty minutes, two blocked shots, and a shot on goal in Wednesday's 6-1 win over the Rangers.
McQuaid (leg) logged 15:12 worth of ice time in Wednesday's 4-1 win over Montreal.
McQuaid (leg) will rejoin the lineup against Montreal on Wednesday, Fluto Shinzawa of The Boston Globe reports.
McQuaid (leg) won't play Saturday against the Red Wings.
McQuaid (leg) is considered a game-time decision for Saturday's game against the Red Wings.
McQuiad (leg) has been ruled out against the Jets on Thursday.