Brown, a former No. 1 overall pick by Washington, is likely out for the season with a chest injury and will be eligible to be a free agent this summer.
"The difficult part of this transaction is having to part ways with several players who we really value and one, in particular, Monta Ellis, who has been instrumental in our organization for the last several years," Riley said. "We wish Monta, Ekpe and Kwame the best of luck in Milwaukee and thank them for their many contributions."
AP Sports Writer Janie McCauley and Josh Dubow contributed to this report.