Fagan was the victim of an horrific tackle by Newcastle's Danny Guthrie in Hull's 2-1 win on Saturday, although he got up on his feet after the incident.
Hull boss Phil Brown says "a red card and three-game ban is insufficient" punishment for Guthrie's act.
Guthrie said he was "very upset" to learn of the injury verdict and vowed to apologise to Fagan in person.
"I want to speak to Craig in person to apologise and wish him a speedy recovery. I hope to be able to do that as soon as possible," Guthrie told Newcastle's official website.
"It was a challenge that came purely out of frustration towards the end of Saturday's game, but anybody who knows me will accept it was totally out of character on my part."
Guthrie was sent off after running several yards to scythe Fagan down as he shielded the ball by the touchline.
"[Fagan's broken leg] was a direct result of a reckless and callous challenge from a player that decided to take the law into his own hands, obviously affected by the situation that's going on at Newcastle," Brown told BBC Radio Humberside.
"It cannot be condoned and it needs to be firmly looked at. I think a red card and a three-game ban is insufficient to deal with somebody who has put a fellow player in a cast