The 23-year-old is expected to resume hitting in the relatively near future and will need to appear in multiple Minor League games before he receives clearance to be activated from the 15-day disabled list.
"I talked to him today. He is throwing the ball around," manager John Gibbons said. "He felt pretty good today. In the next few days, hopefully we'll get him into a game. We're hoping by the weekend.
"He's doing OK. He wishes he could be here that's for sure."
Lawrie suffered the injury on March 6 while playing in an exhibition game for Team Canada prior to the World Baseball Classic. He has gone almost a month without facing pitching, and in many ways he has to start Spring Training all over again.
That's why the Blue Jays have pushed back Lawrie's original timetable. There was a hope he would be ready for Saturday afternoon's game against the Red Sox, but that has since been ruled out.
"His last at-bats were before the WBC, so it has been a month since he really faced live pitching, said Gibbons.
Lawrie suffered a similar injury last season and was forced to miss more than a month. In 2012, Lawrie hit .273 with 11 homers and 48 RBIs while appearing in 125 games.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. This story was not subject to the approval of Major League Baseball or its clubs.