Multiple sources with knowledge of the incident told ESPN and Cleveland.com that Smith threw the bowl at Jones after the team's shootaround.
Smith was suspended for the Cavaliers' loss Thursday to the Philadelphia 76ers at Quicken Loans Arena in Cleveland.
Cleveland announced Smith's one-game ban less than two hours before Thursday's tipoff.
"Cavaliers guard JR Smith has been suspended by the team for one game for detrimental conduct," the Cavaliers said in a statement Thursday. "He will serve the suspension tonight as the Cavaliers host the Philadelphia 76ers at Quicken Loans Arena in Cleveland."
Smith's one-game suspension cost him nearly $95,000, according to ESPN. The 32-year-old is averaging 8.3 points, 3.0 rebounds and 1.9 assists per game, while shooting 36 percent from 3-point range this season.
LeBron James was teammates with Jones on the Cavaliers from 2005 through 2007. James and Smith have been Cavaliers teammates since the 2014 season.
The 14-year NBA veteran has two years remaining after this season on his four-year, $57 million contract with the Cavaliers.