Bird was set to make his major league debut Thursday night at Cleveland. The lefty hitter was batting seventh while Mark Teixeira got a day off.
The Yankees have lost five in a row. Right-hander Nick Goody, who was called up from Scranton/Wilkes-Barre on Wednesday, was sent back to Triple-A. Right-hander Diego Moreno was transferred to the 60-day disabled list with a sore elbow.
The 22-year-old Bird was batting .301 in 34 games at Triple-A. He began the season at Double-A Trenton, where he hit .258 in 49 games. Bird, taken by New York in the fifth round of the 2011 draft, was chosen the Most Valuable Player in the Arizona Fall League last season.