Smith struck Rice on a drive to the basket in the second half of the Knicks' loss to Washington. Rice was whistled for a foul on the play.
Smith was suspended for Wednesday night's 98-95 defeat to Detroit.
The National Basketball Players Association plans to appeal the Smith suspension, arguing that the groin strike was unintentional, a source confirmed. A successful appeal would allow Smith to recoup his lost wages.
Smith's suspension on Wednesday is the latest instance of the league disciplining the 29-year-old.
Smith was suspended the first five games without pay for violating the NBA's anti-drug policy in the 2013 offseason. Last November, Smith was fined $25,000 for sending what the league deemed a hostile tweet to Detroit's Brandon Jennings after Jennings questioned the credentials of Smith's brother, Chris, a former Knicks guard. In January, the 2012-13 Sixth Man Award winner was fined $50,000 for untying his opponents' shoelaces.
In 2012, the NBA docked Smith $25,000 for posting an inappropriate picture of a woman on his Twitter account. He was fined $5,000 for flopping in Game 1 of a 2013 playoff series against Indiana and suspended for Game 4 of the Knicks-Celtics series in last season's playoffs after elbowing Jason Terry in the head.
His total in fines since joining the Knicks in 2011 is $105,000, not including the loss of game checks during his suspensions.
Smith has been vocal about the difficulties of grasping the Knicks' new triangle offense. Through four games this season, Smith is averaging 7.5 points and 4.0 assists in 24.5 minutes. He is shooting 39 percent from the floor.