The league announced the ban Wednesday.
"We are disappointed that Ryan will be unavailable for the first four games of the season," Buccaneers general manager Jason Licht said in a news release. "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 particpate in off-season and preseason practices and games. He can return to the team Sept. 30, after the Buccaneers' Week 4 clash against the Los Angeles Rams.
The 5-foot-11, 189-pound defensive back had 38 tackles, six passes defensed, a forced fumble, a fumble recovery and his first career interception last season. Smith, 25, appeared in 16 games and made six starts in 2018. The fourth round pick in the 2016 NFL Draft had 61 tackles, five passes defensed, two forced fumbles and a fumble recovery in 15 games during his 2017 campaign.
Smith rated as the No. 71 cornerback in the NFL last season, according to Pro Football Focus.