A scan on Thursday showed that the 21-year-old had suffered only minor damage rather than a full tear.
Davies sustained the injury in the opening stages of Derby's Carling Cup defeat at Rotherham on Tuesday evening.
The Rams are not putting a timescale on his absence, but boss Nigel Clough does not expect Davies to be out for too long.
"It is a relief it is not a long-term injury and we have been told the lay-off will be short-term, he won't be out for very long at all," Clough told the club's official website.
"Beyond that we are not prepared to put a date on it or rule him in or out of any matches."