He said Campbell will go through the NFL's concussion protocol and his status will be evaluated during the week.
Campbell was injured midway through the third quarter of Cleveland's 27-11 loss when he was blindsided by blitzing cornerback William Gay.
That led to a fumble that set up a Steelers touchdown.
The Browns are preparing for all outcomes, however, as multiple media reports say they will bring in free-agent quarterback Caleb Hanie as a possible backup for Weeden.
Campbell was in the building Monday morning, and Chudzinski said he seemed to be doing OK. But before Campbell returns to the field, he has to pass the league's concussion tests. That timetable differs for everyone.
Campbell was hit in the face mask by Gay on the play, but no flag was thrown. The Browns will submit the play to the league for review.
"It doesn't seem like they miss that call very much," linebacker Paul Kruger said.
Said Chudzinski, "There were a number of plays, not just that one, that were an issue for us. Hopefully, we'll have Jason back soon."