New York announced the absence on Thursday. Judge sustained a chip fracture of the right wrist (ulnar styloid bone). No surgery has been recommended for the two-time All-Star.
Judge, 26, is hitting .285 with 26 home runs and 61 RBIs in 99 games this season. He led the American League last season with 52 home runs, 128 runs scored and 127 walks. He also led baseball with 208 strikeouts in 2017.
"The Yankees approximate a 3-week time period before Judge can swing a bat in a game situation," the Yankees tweeted.
Judge suffered the injury in the first inning of the Yankees' 7-2 win against the Kansas City Royals on Thursday at Yankee Stadium. The 2017 American League Rookie of the Year took a 93.4-mph fastball to the wrist from Royals righty Jakob Junis.
"I was just trying to go heater away and it totally got away from me," Junis told reporters. "Tried humping up a little extra on it and just really came open and let it go."
Judge stayed in the game initially, recording an infield single in the third inning. He was then seen by a doctor and sent to New York-Presbyterian Hospital for an MRI and CT scan.
Judge was 1-for-1 with a run scored in Thursday's triumph. The Yankees host the Royals at 7:05 p.m. Friday in the Bronx.