Robertson will not be able to pick up a baseball for seven to 10 days, manager Joe Girardi said. With both Robertson and Mariano Rivera unavailable, closing duties will be handed to Rafael Soriano.
"We don't think it's too severe, but it's hard to tell," Girardi said. "Obliques can be tricky."
Robertson felt soreness in his left ribcage after recording two outs on Friday and was unavailable for three games, including Monday's 8-5 Yankees victory over the Orioles. An MRI exam taken on Tuesday in New York revealed the strain.
"It's really disappointing, because it was something I was hoping would just be a real quick recovery, and in two or three days hopefully I'd be back," Robertson said. "It just hasn't gone away. I went and got it checked out today, and it turns out there's a reason why it's not going away."
Robertson took an early-morning train to New York for the exam with team physician Christopher Ahmad and returned to Baltimore in time to see the Yankees' 5-2 loss to the Orioles. He will travel with the club to Toronto so he can continue receiving treatment.
"They said it's very mild," Robertson said. "But it's one of those things where if I kept pitching on it, it's likely to get worse. If it gets worse, I could be out for six to eight weeks or something like that. That's the last thing I want to do."
In a corresponding roster move, the Yankees recalled right-hander Cody Eppley from Triple-A Scranton/Wilkes-Barre. The move is Robertson's first career assignment to the disabled list.
"It's tough for me, but there's nothing I can do about it," Robertson said. "I've never been on the DL before, so this is really weird."
Soriano picked up his second save on Monday and said he welcomes the challenge of the role, while Boone Logan and Cory Wade will be elevated to the later innings in Robertson's absence.
"It's one of the luxuries we have," Yankees captain Derek Jeter said. "We have Robertson, who pitched well; we've got Soriano, who led the league in saves a couple of years ago, so he's familiar with that role. Our bullpen has always been one of our strengths, the way we've looked at it.
"We never anticipated both guys going down like they did, but other guys are going to step up. I think everyone has confidence in Soriano."
Girardi said that he sees himself calling upon Clay Rapada to face left-handed batters in the middle innings, while David Phelps will be utilized both in short relief and for multiple innings. It is also possible that Phelps could be needed to pitch on Saturday against the Reds, with Ivan Nova mending a sprained right ankle.
"We are testing our depth, and time is going to tell if we can sustain what we're doing," Girardi said. "They've done a good job so far. You look at the job those guys have done there, they've been really, really good. I think the distance from your starters becomes maybe a little more important now."