Both players had to be replaced during the first half of Saturday’s Sky Bet Championship opener at Bolton.
Bryson limped off after 21 minutes to be replaced by Jeff Hendrick while Hughes was carried off on a stretcher shortly afterwards, with Ryan Shotton coming on for the England Under-21 international.
After the goalless draw at the Macron Stadium, Derby head coach Paul Clement said: “Craig did his early on with a strong tackle. He wanted to try to continue but it was causing him some discomfort and so it was best he came off.
“With Will, I’m not really sure how the injury happened but he was in a little bit more distress.
“Occasionally, you are going to get one injury. To get two so quickly was disappointing but the squad is well prepared. They all know their jobs.
“Naturally, we didn’t want to make those changes but that is why you have a squad of experienced players.
“We got through pre-season without any real problems, which pleased us. The two injuries against Bolton are not muscle problems. They are both contact injuries and you cannot really do anything about that.”