Per NFL Network's Ian Rapoport, Stewart violated the league's policy on performance-enhancing drugs by testing positive for a masking agent or diuretic.
ESPN's Mike Clay noted in March that Stewart was likely going to be listed at sixth on New York's receiver depth chart. The team signed Terrelle Pryor and Andre Roberts in free agency, joining Jermaine Kearse and Robby Anderson.
After playing three years at the University of Alabama, Stewart was selected in the third round of the 2017 NFL draft by the Jets. He played sparingly as a rookie with just 282 all-purpose yards in 15 games.
If Stewart is suspended for two games to start the 2018 season, he will be eligible to return for the Jets' Week 3 game against the Cleveland Browns on Sept. 20.