Budinger, who has flourished as a perimeter player this season, tore a lateral meniscus in his left knee during the final quarter of Saturday's 87-80 loss to the Chicago Bulls.
The 24-year-old had surgery in Florida on Tuesday to repair the tear and is expected to be out of action for three to four months, the Timberwolves said.
Budinger, who was acquired by Minnesota in a trade with Houston in June, is averaging 11.8 points and 3.5 rebounds in six games this season.
His absence further hampers the Timberwolves who are already without Kevin Love (broken hand), Ricky Rubio (left knee surgery), J.J. Barea (sprained left foot) and Brandon Roy (sore left knee).
Minnesota are second in the Western Conference's Northwest standings after making an impressive 5-2 start despite their glut of injuries.