Wizards president Ernie Grunfeld made the announcement in a statement Tuesday.
Howard was injured Monday night in Washington's win over the Chicago Bulls, only his fourth game with the Wizards since being acquired from Dallas in a seven-player trade on Feb. 13. He collided with the Bulls' Flip Murray with 4:23 to play in the first quarter and stayed on the floor for a minute before being helped off the court by two trainers.
Howard started three games for Washington and scored 14.5 points a game to help the Wizards go 3-1 since the deal, which sent starter Caron Butler to the Mavericks.
Howard has averaged 15.3 points and 6.0 rebounds since his 2003-04 rookie season with the Mavs.
No decision has been announced on whether Howard would have surgery.
"We're disappointed for Josh personally. He did an outstanding job," said Grunfeld. "We feel bad for him. The guys will have to step up in his absence.
"He was excited to be here."
Without Howard, Washington has just 10 players on the active roster. Gilbert Arenas and Javaris Crittenton are suspended for the season for carrying guns in the locker room, and two other players, Zydrunas Ilgauskas and Mike James, are seeking buyouts. Ilgauskas was acquired from Cleveland in a trade for Antawn Jamison on Feb. 16, and Grunfeld said that "we're making progress" in buyout talks.
"We're going to be short-handed," Grunfeld said. "We'll look around and see what's out there, but no one will be able to do what he did."