Pedroia, 35, was moved to the 60-day injured list Monday. He has only played nine games in the last two seasons.
Red Sox team president Dave Dombroski said Pedroia's leave of absence is "indefinite."
"I'm at a point right now where I need some time," Pedroia told reporters. "That's what my status is. ... Right now, I know I need a break from the everyday stresses I've been dealing with."
Knee injuries have bothered Pedroia since he had a "cleanup" surgery after the 2017 season. He was pulled from a rehab assignment earlier this month.
Pedroia is under contract with the Red Sox through 2021. The four-time All-Star is a career .299 hitter and is only 195 hits shy of 2,000 career hits.
"I think the time will give me the right answer of if I can do this," Pedroia said.