Sullinger said he felt some discomfort in the foot the day after Boston closed the first half of the season with a win over the Atlanta Hawks on Feb. 11.
He removed himself from Boston's practice when the team reconvened in Sacramento on Wednesday, and team trainer Ed Lacerte took him for initial tests Thursday that revealed the foot injury.
"It was one of those things where, he said it happened in the Atlanta game, but he couldn't really recall or pinpoint a time of the game," Celtics coach Brad Stevens said Sunday. "But then he just said, as the week went on, he just felt a little bit more discomfort. Then he went through a little bit of practice [on Wednesday in Sacramento], and then said it just doesn't feel right.
"So what we sent him home for was not only to get started on whatever he needs to do from a rehab standpoint, but get more imaging and, from what I've been told, the imaging has shown more significant issues than what we originally thought."
Stevens said he doesn't believe Sullinger will require surgery, but he'll be in a protective walking boot for at least six weeks while allowing the stress fracture to heal on its own.
Asked if Sullinger's playing weight was something to monitor moving forward, Stevens said Boston's medical staff will monitor his rehab and said his focus is on replacing Sullinger's production on the court.
"I think the biggest thing is just to continues to really work on conditioning, because that is important," Stevens said. "He's going to have to do some of that in unique ways. He's going to have to swim, and I don't know whatever options he has while he's in his boot over the next six weeks. I don't know what else they are going to let him do.
"To be candid with you, once I found out, you feel for Jared. But you have to start thinking about how you're going to replace him and these guys here do a great job of helping guys in both their recovery and in staying in shape while they recover."
Sullinger returned to Boston on Saturday for further testing that confirmed a fracture, and the team elected to shut him down with only 53 days remaining in the regular season. The Celtics are 20-32 and (through Saturday) only 1½ games behind in the race for the eighth and final playoff berth in the Eastern Conference.
The loss of Sullinger leaves Boston thin up front. The Celtics were hoping to get second-year big man Kelly Olynyk back shortly after the All-Star break, but he remains sidelined by a right ankle injury that has caused him to miss 12 straight games.
The Celtics will get some help up front after recently acquired Jonas Jerebko joined the team Saturday. Boston has used Tyler Zeller and Brandon Bass in the starting lineup without Sullinger and Olynyk, and Shavlik Randolph, acquired in January, got his first action since joining Boston on Friday night in Sacramento.
Sullinger's rookie season ended after 45 games in 2012-13 due to a back injury. He appeared in 74 games last season. Sullinger was averaging 14.4 points and 8.1 rebounds over 28.7 minutes per game this season.