Hicks suffered the injury in Saturday's 6-4 victory over the rival Boston Red Sox. Hicks reported pain to Yankees trainers after a sixth-inning throw to third base.
"Anything with the elbow makes you nervous, but I'm going to stay positive right now until we get the final decision," Hicks told reporters Saturday night.
The Yankees returned pitcher J.A. Happ from the paternity list in a corresponding move.
Hicks is hitting .235 with 12 home runs and 36 RBIs in 59 games this season. He missed the Yankees' first 40 games with a back injury.
Hicks signed a seven-year contract extension in February. He has only played 130 games in a season once in his career.
New York is 71-39 this season. The Yankees have a 7 1/2 game lead over the Tampa Bay Rays in the AL East Division.