Dr Lou Lewis said he was angry the fight continued after Green was concussed by a controversial blow from Mundine in the first round.
Dr Lewis said he quit because his opinion was overruled by the other doctor in the ring, John O'Neill, and referee Frank Garza.
"Dr John O'Neill was the official fight doctor appointed by the promoter," a spokesman for the Australian National Boxing Federation, which sanctioned the bout, said.
"He attended the pre-fight rules meeting on the morning of the fight with representatives of both camps and the referee.
"Dr Lou Lewis did not."
Green later told reporters he knew he was concussed at the time but had wanted to keep fighting.
He even admitted he was so dazed he combined the names of the doctors and had referred to Dr O'Neill as Dr Lou O'Neill.
The decision to continue the fight for nine more rounds has been criticised by the Australasian Ringside Medicine Association and the Australian Medical Association, doctors warning a further blow to Green could have been fatal.
The ABC has not been able to get a comment from Dr O'Neill.
Green controversially won the fight on points in a majority decision, and Mundine's agent, Khoder Nasser, has confirmed to the ABC an appeal against the decision is being prepared.