Harris pulled up while bowling the fifth ball of his 29th over and immediately pulled off his left boot and sock.
He limped from the ground with the team physio and a decision is to be taken whether he will bat in the second innings as Australia battle to avoid defeat to England in the fourth Test.
"Ryan Harris developed ankle pain during England's first innings and scans have revealed that he has a stress fracture of his left ankle," team doctor Trefor James said in a statement.
"Ryan is likely to require surgery and will consult a specialist in the next 24 hours."
Australia will now need to find a bowling replacement for Harris for next week's fifth Ashes Test in Sydney.
Harris was playing in only his fifth Test match in Melbourne and he also has a degenerative problem in his right knee that needs corrective surgery.
"If I was 21 I'd get it done but I'm not, I'm 31 and it's a 12-month recovery, so for me to have that I think would be the end of my career," he said, after taking 6-47 in the second innings of this month's third Perth Test.
"Basically, the cartilage on the outside of my right knee is going, basically there's not much left and I'm eating through it every time I pound into the crease.
"It's just a management thing and I'm going well at the moment."
Harris had arthroscopic surgery on his right knee earlier this year.