An MCL sprain typically is a four-week injury, which means Strief could be sidelined through the team's Week 5 bye.
Backup Senio Kelemete replaced Strief on Monday for New Orleans, which struggled to ignite its offense versus Minnesota. The 33-year-old Strief had missed just two games since 2013.
Losing Strief for an extended amount of time is a major concern to a Saints' line that is already without left tackle Terron Armstead, who is recovering from shoulder surgery. Rookie Ryan Ramczyk started at left tackle versus the Vikings and gave up a sack Monday night.