John van’t Schip's side will also be without defender Robbie Wielaert (ankle) for ‘a number of matches’ as well as Ben Garuccio, who is also struggling with an ankle injury and is now expected to be absent ‘for at least 10 weeks’.
The club has brought in former Newcastle Jets captain Kew Jaliens on an injury replacement contract ‘for at least six weeks’ to boost its defensive stocks.
In a bitter blow for Melbourne City, Duff will undergo additional scans to confirm the extent of the injury, but it says the early prognosis is that the former Chelsea man may require surgery, ‘which could result in a lengthy lay-off period’.
"We are of course disappointed to learn the seriousness of Damien’s injuries and I know his absence will be a big loss to the team,” Van’t Schip said.
“Damien has brought a lot to the club this season both on and off the pitch and we are going to need other members of the squad to step up while Damien is out of action.”
Wielaert has had surgery on his ankle after being injured in Abu Dhabi during the club’s AFC Asian Cup 2015 break, while Garuccio suffered his ankle injury against Western Sydney Wanderers on 1 February.
Jaliens, meanwhile, will start training with his new team-mates on Wednesday.
"We have decided to bring in Kew as a replacement as he will add some depth at a time where we are missing a number of players due to injury,” Van’t Schip said of the 36-year-old former Netherlands international, who was one of five players sacked by the Jets last month.