The England Under-21 defender suffered the double break on Tuesday evening as he played for Boro's reserves at Morecambe against Blackburn.
Davies was on the end of a challenge from Steven Reid and he was rushed to hospital immediately.
The Teesside-born youngster is believed to have broken his tibia and fibia, but both breaks are thought to be clean.
"It's a terrible blow for Dava to pick up such a bad injury," said Steve McClaren this morning.
"We all wish him well for a full and quick recovery.
"It's unfortunate for him because he was knocking on the door of the first team and had been an important member of the squad all season.
"But he has bags of talent and the strength of character that he will need to bounce back stronger than ever.
"Although it's too early to say just how long he will be out, it will obviously be a long road back. However, he will get all the support he needs from everyone at the club."
It now remains to be seen how long Davies will be sidelined for, but he may struggle to be fit for the new Premiership season in August.
