According to a source, the New York Giants defensive end is going to be out for three to four weeks after an initial test showed a knee injury.
According to a source, the Giants hope that the first-round pick will be ready for the start of the regular season.
The injury occurred in the second quarter of the preseason game when he was cut-blocked by the Cincinnati player.
The former Oregon star told reporters that he was all right after grabbing his knee and walking off the field.
The No.5 pick in this year's NFL draft had a strong summer and had a quarterback pressure early in the contest.
The Giants are expecting big things from Thibodeaux, who has been working with the first string defense since the start of the spring.
The potential No. 1 prospect in college football was Thibodeaux, who had 19 sacks in his career at Oregon.
Jordan was a contributor to this report.