Montgomery slipped before he took a handoff from quarterback Mitchell Trubisky and went to the ground. He got up holding his left leg and appeared to be in serious pain.
He limped off the field and was carted back to the team facility about 10 minutes later.
Nagy said he did not know the severity of Montgomery's injury. The running back is undergoing further evaluation.
Nagy said the club plans to explore all options in the aftermath of Montgomery's injury.
"You try to stay as positive as you can," Nagy said. "You don't know, really, what the answer is and where things are at. And then there's different again, we talk about contingency. This is the year of the contingency, so now this is one without COVID as an injury. What are our options? Do we like where we're at right now or do we feel like we need to go outside of the building? That's all stuff that we'll discuss. Whatever we do, we'll do it so that it helps us. For sure, we've got to look at all that."
Montgomery led the Bears with 889 rushing yards and six touchdowns in 2019, his rookie season.
Nagy said he loves Montgomery's "ceiling."
"They don't make many guys the way they make David Montgomery. He's a special player," he said. "We believe in him. We were hoping he would slip to us in that position [third round] we were in the 2019 draft. He's worked really hard. He knows how we do things. He bought into it. We're just knocking on wood hoping that he's going to be OK. We really think his future is super bright and we want to have a long career with him."