Brumfield suffered an injury to his left knee in the first quarter of the Tigers' 38-21 win over Louisiana Tech on Saturday.
"We don't know when Garrett will be back," LSU Ed Orgeron said Monday. "I don't know that yet."
Brumfield is the second offensive line starter LSU has lost to injury, but the Tigers have adjusted on their way to a 4-0 start.
Starting right tackle Adrian Magee suffered an undisclosed injury in the Tigers' season-opening win over Miami but could be back this week.
Orgeron said Magee and left tackle Saahdiq Charles are questionable to play against Ole Miss.
Orgeron said freshman offensive lineman Chasen Hines was "excellent" filling in for Brumfield.