The Bears placed Gould on injured-reserve on Tuesday and signed veteran kicker Olindo Mare to a one-year contract.
Chicago also placed cornerback Sherrick McManis and safety Craig Steltz on IR. McManis, a Richwoods graduate, is out with a knee injury. Steltz is sidelined with a chest injury.
The Bears signed linebacker Jerry Franklin to a two-year deal, elevated receiver Joe Anderson from the practice squad and waived offensive lineman Andre Gurode.
Gould, who ranks among the most accurate kickers in league history, strained his left calf in warm-ups before Sunday's loss at Minnesota, and punter Adam Podlesh handled kickoffs in his place.
Gould kicked the extra point after both of Chicago's touchdowns and tried on onside kick late in the game.