NEW YORK — Yankees second baseman Starlin Castro may miss the All-Star Game because of his strained right hamstring.

Castro went on the disabled list June 27, and New York manager Joe Girardi said Castro won't start running hard until Thursday.

"I don't know if we'll have him back before the break," Girardi said before Tuesday's 4-1 loss to Toronto.

Girardi said it would be "fairly important" for Castro to play again for the Yankees in order to appear in the All-Star Game at Miami on July 11. Players elected Castro to a reserve spot on the roster, his fourth All-Star selection. Castro said he will attend, even if he isn't on the active All-Star roster.

New York activated left-hander CC Sabathia and right-hander Adam Warren from the disabled list Tuesday and optioned right-handers Bryan Mitchell and Domingo German to Triple-A Scranton/Wilkes Barre.

Sabathia, who lasted just 2 2/3 innings in the loss to the Blue Jays, had been on the DL since June 14 because of a strained left hamstring. Warren, who retired his only batter Tuesday, went on the DL two days later with right shoulder inflammation.

Right-hander Luis Cessa will move to the bullpen. He allowed five hits in 4 2/3 scoreless innings against the Blue Jays.

"We wanted to continue to keep Mitchell going," Girardi said. "We thought he was making some really good strides in his starts down in Triple-A and he was starting to get over that hump and become aggressive, and we want that to continue because you know at some point, a lot of times you might need another starter, and we're preparing him for that."

Girardi said the Yankees still do not know exactly what ails designated hitter Matt Holliday, who has been on the DL since June 25 with a viral infection.

"I don't think we have all the test results back yet," he said. "I don't have a clear plan of when he'll be back."

After the game, the Yankees designated first baseman Chris Carter for assignment for the second time this season. Carter went 0 for 2, lowering his batting average to .201, and dropped a throw from shortstop Didi Gregorius, giving Jose Bautista an infield single.

Girardi's frustration was evident.

"Originally our plan was Greg Bird to be our first baseman, and he's hurt," Girardi said. "We called up Tyler Austin and he got hurt. So it is what it is and we'll continue to go day by day."

A short while later, the Yankees cut Carter and said they will bring up infielder Ji-Man Choi on Wednesday from Scranton/Wilkes-Barre, where he is hitting .289 with eight homers and 43 RBIs. Choi made his big league debut with the Los Angeles Angels last year and hit .170 with five homers and 12 RBIs in 54 games.

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