The move is retroactive to Saturday. Williams jammed his right shoulder while diving back to first base on a pickoff attempt Friday. He initially remained in the game but was replaced in the next inning.
Williams, 23, is ranked by MLBPipeline.com as the Yankees' No. 26 prospect. He made his Major League debut June 12 against Baltimore and hit .286 in eight games.
"Like probably most young kids, he'd probably say that he was ready before he was actually ready," Yankees manager Joe Girardi said. "We don't want to rush him back. So we just thought, you know what, you're down for 15 days, let's clear it up and you'll be back.