Rivers, who was New England's top pick in the 2017 NFL draft as a third-round choice out of Youngstown State, returned to Boston on Thursday and had an MRI. He will get a second opinion to determine whether surgery is necessary.
NFL.com first reported the results of Rivers' MRI.
Rivers went down on a kickoff coverage drill Wednesday in a joint practice with the Houston Texans at The Greenbrier in White Sulphur Springs, West Virginia. Head athletic trainer Jim Whalen examined Rivers' left knee on the field.
The Patriots traveled to Houston for Saturday's preseason game.
Rivers, who was selected 83rd overall, was projected to be part of a rotation at defensive end, which was arguably the Patriots' thinnest position entering training camp.
Trey Flowers, who led the Patriots with seven sacks last season, tops the depth chart at the position. After Flowers, there is a notable drop, which will likely lead the team to explore a free-agent signing or trade. Another option could be to try to entice Rob Ninkovich out of retirement.