Bradshaw is facing a one-game suspension for violating the league's Policy and Program on Substances of Abuse, a league spokesperson confirmed to Around The NFL on Monday.
The running back pleaded not guilty to a marijuana possession charge in February.
On a recent edition of the Around The NFL Podcast, we discussed Bradshaw as the one unsigned player most likely to find a team once veterans can be signed to non-guaranteed contracts after the first week of the season.
Although Bradshaw's litany of lower-leg injuries have understandably scared teams off, he has been among the most efficient tailbacks in the league when healthy.
He led all backs in receiving touchdowns (six) last season despite missing the final six games.
We still expect Bradshaw to play in 2015, but this is another reason for interested teams to delay a signing until mid-September.