Alkins suffered the injury on Tuesday afternoon during voluntary activities with teammates.
Alkins, a 6-foot-5 shooting guard, averaged 10.9 points and 4.9 rebounds last season. He tested the NBA draft waters after the season ended, but he decided in late May to withdraw his name and return to Tucson for his sophomore season.
Alkins is projected as a second-round pick in the 2018 NBA draft, according to ESPN's Jonathan Givony.
Freshman Brandon Randolph, an ESPN 100 recruit, should see an increase in minutes while Alkins is out.
Arizona has a strong case to be considered the preseason No. 1 team in the country, as it returns Alkins, Allonzo Trier and Dusan Ristic. The Wildcats also have an elite recruiting class led by top-three prospect DeAndre Ayton.
Arizona opens the season on Nov. 10 against Northern Arizona. It's unclear when Alkins will return. Pac-12 play begins on Dec. 30 against Arizona State.
The news came a day after Arizona made national headlines over an FBI investigation that resulted in the arrest of 10 people, including Arizona assistant coach Emanuel "Book" Richardson.
According to FBI documents, Richardson allegedly accepted more than $20,000 from financial advisers in order to steer players toward them after college.