Barrie was scratched for the 12th straight game Tuesday in a 4-3 win over the Predators.
Barrie scored a goal on two shots in Thursday's 4-3 overtime loss to the Bruins.
Barrie signed a one-year, $1.25 million contract with Calgary on Thursday, per Salim Nadim Valji of TSN.
Barrie will link up with Calgary for training camp on a professional tryout agreement, the team announced Tuesday.
Barrie (healthy scratch) was almost dealt to the Flames at the trade deadline, but ultimately a deal did not get done, Emma Lingan of The Hockey News reports.
Barrie (upper body) will return to the lineup Saturday against Arizona, Nick Kieser of 102.5 ESPN Nashville reports.
Barrie (upper body) won't play Monday against Vegas, per Zach Gilchriest of the Predators' official site.
Barrie (upper body) is expected to miss Friday's game against Dallas.
Barrie (upper body) is expected to miss his fifth straight game Thursday versus Calgary,
Barrie (upper body) will not play Saturday versus the Capitals, Zach Gilchriest of the Predators' official site reports.