Josh Katzenstein of the Times-Picayune reported the update Friday.
Vereen was competing for a roster spot after signing with the Saints as a free agent in July. The team will be without fellow rusher Mark Ingram for the season's first month because of a four-game suspension.
The 29-year-old University of California product tallied nine carries for 22 yards and a team-high nine catches for 41 yards during the preseason.
His receiving prowess made his a third-down weapon during previous stints with the New England Patriots, who selected him in the second round of the 2011 NFL draft, and New York Giants. He has more receiving yards (1,865) than rushing yards (1,489) across seven NFL seasons.
A timetable for his complete recovery wasn't immediately announced.
Meanwhile, Alvin Kamara is set to get a lion's share of the touches in the New Orleans backfield until Ingram returns to the active roster.
Jonathan Williams, Boston Scott and Trey Edmunds are the other options at the position.