Per ESPN's Dave McMenamin, the Cavaliers issued the ban after identifying the person and will review the penalty in one year.
Microphones in Quicken Loans Arena picked up the fan's remarks in the fourth quarter of San Antonio's 110-94 win.
"Hey, Jamaican dog. They want their bobsledder back," the fan yelled at Mills, via Benyam Kidane of Sporting News. "Hey Mills, Jamaica just called; they want their bobsledder back."
Mills addressed the situation on Twitter:
Patrick Mills @Patty_Mills
Thanks @thats_Z_Truth. I am a proud Islander. Like my Jamaican Brothers, me & my family in the islands of the Torres Strait have experienced racial slurs for decades. Hope your efforts will enlighten this confused, hateful fan. #BlackHistoryMonth https://t.co/yH3nKlGv4A
A Cavaliers spokesman told Joe Vardon of Cleveland.com security officials were reviewing the tape to identify the speaker.
Mills, 29, was born in Australia. His mother, Yvonne, and her siblings were forcibly removed from their family when she was two years old because her father was white and her mother was an Aboriginal Australian.