Bryson came off midway through the second half of the Rams' 2-0 win at Bristol City at the weekend and the midfielder is a doubt ahead of the home game against Hull on Friday night.
"We didn't substitute Craig because we felt we were comfortable and the game was over at 2-0, it was because he said his knee was too sore," said Clough.
"When he initially did it, the physio said it could be anywhere between two and six weeks. So he will just have to get through the best he can, but with three games in nine days coming up it is going to be difficult.
"We will ease him through this week. He might do a little bit (of training) on Thursday but there is always that risk when you do train of opening the knee up again.
"So it is about getting the balance. He's got to do something but have as little contact as possible."
Defenders Mark O'Brien (cramp and illness) and Gareth Roberts (calf), midfielder Will Hughes (ankle) and striker Conor Sammon (calf) are also nursing injuries from the weekend.
- Sports & Recreation