Melbourne released a press statement on Monday saying the surgery had been a success.
A plate and screws were insterted to realign Green's mandible bone.
The Demon utility sustained the injury after clashing with Tiger youngster Alex Rance at the 24-minute mark of the opening term. He immediately left the field and was taken to Epworth Hospital.
"From what I understand, Brad's got a broken jaw," coach Dean Bailey said on Sunday.
"It's really disappointing, because he's an utter professional and a very, very important player in our leadership group."
Despite the loss of one of Melbourne's most influential players, Bailey was pleased his charges stepped up against the Tigers.
"There's no question they all had to give a little bit extra, because we lost a very, very good player, who has arguably been our best player for three weeks, Brad Green," he said.
"He's a fantastic bloke and he trains hard and he's incredibly professional with his attitude and he's a terrific player for us.
"The players rallied around him and all dug an extra two or three per cent, which they've all got in them, but it just had to come out today."
Meanwhile, Bailey said skipper James McDonald was a chance to play in next Sunday's clash against Adelaide at the MCG.
He said that Russell Robertson and Matthew Whelan were two weeks away from returning to the seniors.
"He's keen to come back Russell, there's no doubt about that, but I think definitely one … but we want to play him when he's ready to go and we don't want to rush him into it," Bailey said.
