Going into the fourth round match, Federer was the heavy favourite to get through to the quarter-finals and face Novak Djokovic.
After winning the first set 6-3 and going a break up in the second set, it appeared to be a foregone conclusion that Federer would meet Djokovic for the 47th time.
But Millman pegged Federer back and won the set 7-5 before winning two tie-break sets to beat the Swiss star and reach the last eight of a Grand Slam for the first time.
Observers of the match felt Federer struggled with the humid conditions and he admitted after the match that he felt he could not breathe at times.
And ESPN reporter Chris McKendry revealed Federer was initially unable to get to the locker room as he required immediate treatment.
She said: “We follow the players all the way to the locker room, he didn’t get there.
“He quickly came off the court and went to a door on the right – a holding room usually for players.
“That is as far as he got.
“Before he went in there and needed to cool down, receive some treatment and make sure the medical start had a look at him.”
McKendry’s colleague Mary Joe Fernandez, who is the wife of Federer’s agent Tony Godsick, revealed the 37-year-old struggled with the conditions.
She added: “It was tough, the conditions for the first time got to Roger.
“I did get to see him afterwards in the holding room and he was not well.
“He was not feeling well, he took a long time to lay down [and] try to get his breathing under control.
“It was difficult for him. It was tough for him on the court because Millman was fit as a daisy.
“He looked like he was ready to go another could of sets.”