Quarterback EJ Manuel will be behind center in the absence of Carr, who sustained the injury while being sacked during third quarter of Oakland's 16-10 loss to the Denver Broncos on Sunday. He was taken down by Adam Gotsis and received an inadvertent knee to the back from fellow defensive end Shelby Harris.
The 26-year-old Carr remained on the turf for several minutes as team trainers and medical personnel came on to the field to assist him.
"(Carr's absence) could be as short as two weeks -- it could be longer," Del Rio told reporters before noting that he could be out as many as six weeks.
Carr is 79 of 109 for 753 yards with seven touchdowns and two interceptions in four games for the Raiders (2-2), who have lost two in a row.
Manuel, 27, completed 11 of 17 passes for 106 yards and an interception on Sunday.
Oakland hosts the Baltimore Ravens (2-2) on Sunday at 4:05 p.m. ET.