Barr's injury is expected to end his season, coach Mike Zimmer said Monday.
Barr, a four-time Pro Bowl selection, was limited to 16 snaps in Week 2 and is the third player the Vikings have moved to IR since the start of the season, joining defensive end Danielle Hunter (neck) and left guard Pat Elflein (thumb).
"Anthony was our first draft pick that we had when we came here," said Zimmer, the Vikings' head coach since 2014. "A big, integral part of the defense. Good leader, great guy. It's tearing him up inside that he's not going to be able to play but it is what it is and we've got to move on."
Fourth-round rookie Troy Dye replaced Barr on Sunday before suffering an ankle injury. The injuries to both Barr and Dye led to Ryan Connelly making his debut two weeks after being claimed by Minnesota.
"I thought Troy came in and did some good things," Zimmer said. "He had a couple missed tackles, but he ran pretty well. Once Barr went out, it got a little confusing because Eric [Kendricks] was trying to get the calls from the headset and then make the calls and get guys lined up. So that got a little confusing. [Eric] Wilson did fine. We've still got a lot of things we have to work on with those guys, but we anticipate that they'll continue to get better."
Minnesota's linebacker depth will undergo a stiff test as the Vikings prepare for Derrick Henry and the Tennessee Titans. Wilson, the team's No. 3 linebacker, will step into an every-down role opposite Kendricks. Dye and Connelly round out the linebackers currently on the active roster, with veteran Hardy Nickerson Jr. available for call-up from the practice squad.