Big 12 Commissioner Bob Bowlsby said Smart, who leads the 19th-ranked Cowboys in scoring at 17.5 points per game, was sanctioned after an incident Saturday in Lubbock, Texas, near the end of a loss to Texas Tech.
With 6.2 seconds left, Smart sailed into the crowd seated behind the basket after fouling the Red Raiders' Jaye Crockett. Smart got up and was heading back to the court when he turned to face a male fan, then lunged toward the man and shoved him.
The star sophomore was given a technical foul and later was escorted to the locker room.
"Mr. Smart's actions were a clear violation of the Big 12 Conference's sportsmanship and ethical conduct policy," Bowlsby said. "Such behavior has no place in athletics, and will not be tolerated."
"I want to apologize to the fan, my teammates, my coaches and my family," said Smart during a Sunday press conference.
Smart said the fan, identified as Jeff Orr of Waco, Texas, called him a racial slur, but Texas Tech released a statement indicating its review of video and audio from the incident revealed no slur.
Orr has voluntarily agreed to not attend a Texas Tech home or away basketball game for the remainder of the season, the school said.
Smart will miss three key conference contests for struggling Cowboys, who have dropped four straight.