The 23-year old suffered the terrible injury in Saturday's 1-1 draw with Southampton at Pride Park and required plates and screws to be inserted.
Rams boss Nigel Clough says the club is right behind leading scorer Davies who continues to have bad luck with injuries.
"Steven has been so unlucky with injuries at Derby County and we're all gutted for him," Clough told the club's official website.
"If anyone is due a bit of luck, it's him.
"It was an innocuous incident as well with no intent from the Southampton player at all.
"He is going to be out for the best part of 12 weeks and we will miss him."