"He sustained the injury earlier this month while training," the team said in a brief statement, adding that further updates "will be provided as appropriate."
Irving, an eight-time All-Star, averaged 22.2 points and 5.1 assists per game in the post-season, when the Mavs fell to the Boston Celtics in five games in the championship series.
Irving dealt with a hand injury during this past season, when he sprained his thumb on his right shooting hand.
He broke his right hand in 2012 before his second NBA season with the Cleveland Cavaliers, suffering the injury when he slapped his hand against a wall during an NBA Summer League practice.
Irving, 32, is coming off his first full season with the Mavericks. He and star teammate Luka Doncic will be hoping the arrival in free agency of Golden State Warriors star Klay Thompson will see them contending again for a title in the upcoming season.
