Blue Jays manager John Gibbons announced the news on Monday.
Lawrie felt discomfort in his left side during an exhibition game with Canada's World Baseball Classic team against the Cincinnati Reds on March 6.
He said Monday that he's not sure when he will be able to return.
"I can't give a timetable, it's so hard," Lawrie said, according to MLB.com. "Everyone asks me every day, 'How does it feel?' It feels fine, to be quite honest with you, but it just does not feel like my other side and that's a problem. It raises a red flag to myself.
"You can't go out there and expect to be who you are if everything doesn't click. Sure, you could go out there and suck it up for a few games, but what happens when I have to go back to the manager and say 'Yeah it's sore,' and then I have to go through this whole process again?"
According to MLB.com, Lawrie's disabled list stint can be backdated to March 22, meaning the earliest he'd be eligible to make his season debut would be Toronto's fifth game of the season.
Utilityman Mark DeRosa is expected to get the bulk of the playing time at third base in Lawrie's absence.
Lawrie batted .273 with 11 home runs and 48 RBIs in 125 games for the Blue Jays last season.
Information from The Associated Press was used in this report.