The forward was forced off after only 10 minutes at the Don Valley Stadium and is set to have a scan on Thursday.
"You have to wait 24 hours to get a proper assessment on a hamstring strain, so at this stage we can't be certain on how bad it is," Clough told Derby's official club website.
"It was a blow on the night to lose Steven and it is a blow for the weekend if he is not available. He has been one of the big positives during the pre-season campaign and his commitment and
attitude was there for everyone to see against Peterborough.
"Hopefully it will be good news and a very short lay-off for him."
Davies was Derby's only fully-fit forward with Giles Barnes (Achilles) and Chris Porter (hip) long-term absentees, Rob Hulse still recovering from groin surgery and Luke Varney and Kris Commons not match-fit after illness and a hamstring injury respectively.