He will get an MRI on Monday, and if the test is negative, he intends to play in week 13.
Rodgers, in more than half the game, completed his night 11 of 16 passing for 140 yards, two touchdowns and two interceptions.
Rodgers left Sunday night's 40-33 win over the Philadelphia Eagles in the third quarter and did not return. He was replaced by Jordan Love.
Love took over on the ensuing drive and threw a quick 63-yard touchdown pass to Christian Watson. Love finished the game completing 6 of 9 passes for 113 yards.
At 4-8, the Packers' playoff chances are long, but Rodgers said he wants to keep going as long as he can.
"As long as we're alive in the math, I'd love to be there," Rodgers said.