School officials said the 75-year-old Brown wasn't feeling well and dealing with some symptoms of vertigo. Brown has had similar issues in the past.
Associate head coach Tim Jankovich directed the team in the second half against UCF.
The Mustangs, one of two undefeated Division I teams remaining, were playing the 15th of their 30 games this season.
SMU is banned from postseason play because of NCAA sanctions handed down last fall. That included a nine-game suspension at the start of the season for Brown, during which Jankovich also served as head coach.