Trout, who turns 27 on Tuesday, hasn't played since injuring his wrist while sliding on a steal attempt Wednesday in Tampa. He said Saturday night that he still has soreness in his wrist when he swings and throws.
After he was evaluated Sunday, manager Mike Scioscia chose to keep him out of the series finale against the Indians.
The Angels open a three-game series Monday in Detroit.
Trout had expected to be back earlier, but his wrist has not responded to treatment as hoped. X-rays and an MRI revealed inflammation. Trout said following Saturday's game that it's been "frustrating. You don't want to be sitting on the bench watching your team out there."
Eric Young Jr. again replaced Trout in center field for Sunday's game.
Trout is batting .309 with 30 home runs in 109 games.
The Angels also have designated third baseman Luis Valbuena for assignment, the team announced.
Rookie Deck McGuire was called up from the minors to start Sunday's game against the Cleveland Indians. McGuire is 0-1 with a 5.94 ERA in seven appearances this season. He has made three starts for Los Angeles, never pitching longer than 3 1/3 innings.