The injury will require surgery, which has yet to be scheduled.
"We'll know more about the extent of how long he will be out after surgery," manager John Farrell said. "At this point, with four months remaining, I wouldn't suspect it to be season-ending."
It's unfortunate timing for Lavarnway, who was recalled on Monday for his first stint with Boston this season.
However, the move will give Hassan, a Quincy, Mass., native, the opportunity to make his Major League debut. In 45 games with Pawtucket, Hassan hit .217 with 10 doubles, one home run and 19 RBIs.
"I feel real fortunate, really excited. It's really hard to put into words at this point," Hassan said. "Certainly a lot went into it. In the moment it's tough to sum up, but I'm really happy.
"There were some challenges during the season, but lately things have been going a lot better and I've been feeling a lot better offensively and defensively."
Farrell isn't focused so much on Hassan's offensive capabilities, but his ability to play multiple positions.
"With the injury, we needed another right-handed bat. The versatility is similar to Ryan's. He can play first base, but also move to the outfield. He's moved around to two corner-outfield spots and also played a handful of games at first base. It is an opportunity for him to come in and make his Major League debut."
The Red Sox's active roster seems to be a revolving door as of late, with four roster moves made in the last week.
"We know who is here today and it changes the roster," Farrell said. "We'll look to do the best we can and mix and match to put our guys in a position to succeed. We are tapping into the depth, just like we did last year."