Per Shams Charania of The Athletic and Stadium, Mirotic will miss at least two to four weeks after being diagnosed with a slight fracture in his left thumb.
Mirotic scored 23 points and grabbed six rebounds in 24 minutes in Tuesday's 115-101 win over the Los Angeles Lakers.
Milwaukee's depth will be tested over the final 11 games of the regular season and into the playoffs.
Giannis Antetokounmpo sat out against the Lakers with a sprained right ankle. Malcolm Brogdon is expected to miss six to eight weeks after being diagnosed with a minor plantar fascia tear, per ESPN's Adrian Wojnarowski and Malika Andrews.
The Bucks acquired Mirotic as part of a three-team deal involving the New Orleans Pelicans and Detroit Pistons on Feb. 7. The 28-year-old has averaged 11.6 points and 5.4 rebounds for Milwaukee in 14 games since the trade.
The Bucks have already clinched a playoff berth and have a three-game lead over the Toronto Raptors for the No. 1 seed in the Eastern Conference. They have 11 games remaining in the regular season, with their final game three weeks from Wednesday (April 10) against the Oklahoma City Thunder.