Santos was injured during pregame warmups before Sunday’s loss to the 49ers. He made two extra points, but punter Pat O'Donnell handled kickoffs.
The Bears signed Santos last month to replace Connor Barth.
Nugent, 35, made 7 of 9 field goals in four games with the Cowboys while filling in for Dan Bailey after Bailey injured his groin. He spent seven seasons with the Bengals.
Nugent has converted 80.7 percent of his career field-goal attempts.