Francisco suffered the injury while running out a ground ball during Friday night's game against Tampa Bay. The strain isn't as severe as initially feared, and Francisco has already resumed swinging a bat.
The six-year veteran is expected to open the year as a reserve outfielder, and he should be ready in time for Opening Day.
"Right now, we're very optimistic about that," Blue Jays manager John Farrell told reporters on Sunday morning.
"This is on the shorter range of the time that could be missed here. We still think it's going to be that five-to-seven-day period, but he has responded very well to treatment, all day treatment yesterday."
Francisco was acquired in an offseason trade with Philadelphia. Last year with the Phillies, he hit .244 with six home runs and 34 RBIs in 100 games.