Smith has spent his three-year career in Tampa Bay after the Buccaneers selected him in the fourth round of the 2016 draft out of North Carolina Central.
The 25-year-old appeared in every game for the Bucs last season, with six starts. He had 38 tackles after finishing with a career-high 62 tackles in 2017.
"We are disappointed that Ryan will be unavailable for the first four games of the season," Buccaneers general manager Jason Licht said in a statement. "We do extensive training and education for our players regarding the league's polices, but ultimately each individual is responsible for what they put in their bodies."
Smith is eligible to return to the active roster the Monday after Tampa Bay's Week 4 game against the Los Angeles Rams on Sept. 29. He may participate in Tampa Bay's offseason practices and preseason games before his suspension begins.