The early belief is that Thibodeaux's injury is not severe.
"I'm all right. I'm good," Thibodeaux said leaving the stadium under his own power with only a slight limp.
"We're good. Good news," he added later.
Thibodeaux will undergo further tests on Monday. That will ultimately determine how much time he will have to miss.
It didn't look promising when the injury happened given the way Thibodeaux was hit and his reaction. He went down after getting cut-blocked by Bengals tight end Thaddeus Moss in the second quarter and immediately grabbed at his right knee.
Trainers and doctors attended to Thibodeaux near the 20-yard line. The cart came out for Thibodeaux, but he got up and walked right past it. The rookie went into the blue medical tent before emerging with a smile and some laughs. He walked the length of the sideline before heading inside with a trainer.
"I can't answer [that anything severe is ruled out] yet," coach Brian Daboll said. "They'll be doing tests [Sunday night], MRIs and stuff like that and get a better feel for it in morning. You hope not. Don't have an answer for that yet."
Thibodeaux seemed to be taking an optimistic approach. He relayed to teammates after the Giants' 25-22 preseason win over the Cincinnati Bengals that it wasn't something that would ruin his rookie season.
Thibodeaux gave off a positive impression.
"He's always in good spirits. I hope he's OK. I talked to him. He's walking on it. Said he was fine," defensive lineman Dexter Lawrence said. "Probably something that will just take time to heal a little bit. I don't really know what it is. I'm not a doctor."
Thibodeaux was the fifth overall pick in the 2022 NFL draft out of the University of Oregon. He was having a strong summer and had a quarterback pressure earlier in Sunday's contest.
The Giants are expecting big things from Thibodeaux this season. He has been working with the first-string defense since the start of OTAs in the spring.
Thibodeaux had 19.0 sacks in 30 career games at Oregon. He went into last season as the potential No. 1 overall prospect in college football.