Castro's strain is the least severe of three possible grades, but such an injury typically takes at least two weeks for recovery.
Considering the Yankees have just 13 games remaining after Sunday's series finale against Boston, manager Joe Girardi said that he would consider it "a bonus" if Castro appears in another regular-season game.
"It's hard to say. It really just depends on how quickly he heals," Girardi said. "Hopefully it's not too long. Hopefully it's not more than a week, but still I think that's probably pushing it. But you're hoping that he heals quick."
In Castro's absence, Girardi plans to use Ronald Torreyes and Donovan Solano at second base. Ellsbury is considered day to day, and Girardi said that it is possible that he could play in the upcoming series against the Rays at Tropicana Field, which begins on Tuesday.
"We'll try to get him back as soon as we can, but being a center fielder, you have to be able to run," Girardi said.
Both players remained in New York for Sunday's series finale against the Red Sox, as they are receiving treatment at Yankee Stadium before joining the team in Tampa, Fla. on Tuesday.
Owning a slash line of .273/.304/.439, Castro is the Yankees' leader in hits (153), total bases (246) and RBIs (69), and his career-high 21 home runs are more than any player on the current roster.
"It's not what you want," Girardi said. "He's been swinging the bat extremely well, driving in runs, hitting home runs. He's been playing good at second base, but it's reality. Sometimes you play all these days in a row, things can pop up."
Ellsbury is batting .265/.327/.382, leading the club with 18 steals in 26 attempts.
The Yanks also were without third baseman Chase Headley for Sunday's game. Headley experienced lower back stiffness in Saturday's loss, but stayed in the game because the Yankees had already used Rob Refsnyder and Torreyes off their bench.
"He said that he probably would have said something during the game but he noticed that Ref was out, Torreyes was in, and there really wasn't any place to go," Girardi said. "After the game, he was really stiff, and he's still stiff today."