The Los Angeles native has a history of knee problems because of a joint condition and had been dealing with side effects from a previous surgery for a few months, sources told ESPN's Jeff Borzello.
Williams also missed some action in January and February due to knee soreness.
"I've overcome obstacles before in my life and will work with our strength and medical staffs to overcome this one," Williams said in a statement obtained by Borzello. "I'm dedicated to continuing my work in the classroom as a student, and I look forward to supporting my teammates and coaches as I spend this season focusing on my health."
Williams was the 39th-ranked recruit on the ESPN 100 for 2018.
The sophomore started 21 games for the Wildcats last season, averaging 11.4 points and 3.4 assists per contest.
"The news of Brandon’s season-ending surgery is beyond disheartening," head coach Sean Miller said in a statement. "All of us that comprise Brandon's Arizona basketball family, as well as our own loyal and passionate fan base, will rally around him and support him as he begins his journey to recovery."
Five-star recruits Josh Green and Nico Mannion are expected to step in for Williams in the backcourt.
The Wildcats posted a 17-15 record last season and missed the NCAA Tournament for the first time since the 2011-12 season.