Miller is entering his second season as head coach after taking over for Brad Stevens. Butler finished 14-17 last season in its first year in the Big East Conference.
Butler announced his leave of absence in a press release from vice president and director of athletics Barry Collier.
"Brandon Miller has requested a leave of absence for medical reasons, which the university has granted," stated Collier. "We are not in a position to further elaborate and we ask that everyone respect Brandon's privacy."
Assistant coach Chris Holtmann was named interim head coach. Before joining Butler last year, Holtmann was the head coach at Gardner-Webb University where he was named Big South Coach of the Year in 2013.
Butler starts practice on Saturday and opens the regular season on Nov. 15 against Maine.
- Paul Palladino