Robertson was placed on the 15-day disabled list Tuesday with a strained muscle in his left rib cage. The right-hander was working as the fill-in closer for Rivera, who is likely sidelined for the season after tearing a knee ligament May 3.
Robertson finished five games this season and was 0-1 with a 2.51 ERA and one save. He had not pitched since Friday because of discomfort in his rib cage, an injury diagnosed Tuesday as a strained oblique muscle.
"We don't think it's too severe, but it's hard to tell," manager Joe Girardi said. "Obliques can be tricky. We expect him not to pick up a baseball for probably seven to 10 days, and then we'll see where we are after that."
To fill out the bullpen, New York recalled right-hander Cody Eppley from Triple-A Scranton/Wilkes-Barre.
Rafael Soriano, who earned a save Monday night in Baltimore, will become the new closer.
"We lost Mariano first. The bullpen will do whatever we have to do," Soriano said. "Now, with two guys down, it's not easy for us."
Soriano was 2-0 with a 2.57 ERA and two saves entering Tuesday night's game against the Orioles.
Although no one told Soriano he's been assigned the stopper's role, the right-hander said pitching coach Larry Rothschild has indicated Soriano will be finishing games.
Asked whether he was eager to fill the role, Soriano responded, "Oh, yes."
Despite losing Rivera and Robertson, Girardi was confident the Yankees' bullpen would be effective.
"They have been used a lot lately, but we think we have the guys that can get it done," the manager said. "Guys' roles have just increased a little bit, but we're not going to abuse them and ask too much."