He is expected to miss three to four weeks.
Mumford suffered the injury when he clashed with Adelaide's Jared Petrenko during the Swans' 77-point win at AAMI Stadium, with the ruckman substituted at three quarter-time.
Swans coach John Longmire admits the timing is disappointing for Mumford as he was beginning to return to his best form.
"It is disappointing for him, he's probably just got going again and now he misses another slab of footy," Longmire said.
The 26-year-old sat out the round seven match against Hawthorn with a groin strain, but had been building in recent weeks, putting in an excellent performance against Essendon last week.
Mike Pyke will continue to hold down the rucking duties in Mumford's absence, with Jesse White a chance to retain his place as back-up after a decent performance against the Crows.
Kurt Tippett is also set to make his Swans debut against Port as a permanent forward.
With his 11-game suspension now over, Longmire said Tippett was every chance to line-up for the Swans at AAMI Stadium, even before Mumford's injury.
The former Crow will take part in an intraclub match during the Swans' bye on Saturday to find some touch before almost certainly making the trip back to his former home ground in Adelaide.
But Longmire will keep him out of the ruck as he regains his match conditioning.
"He's a big chance to play, but we'll confirm it next week," Longmire said.
"He's still got a couple of training sessions we want him to get through and pull up well from, he's been doing that pretty well to date, but he's obviously a big chance to play.
"We've just looked at his work load the last six to eight weeks and he's had a pretty solid training block.
"We'll confirm it next week, one if he plays for sure, and he's a big chance to, and also how many minutes he plays."
In other injury news, Lewis Jetta appears likely to miss just the one game after he was rested from the Adelaide game with shin soreness.
Sam Reid (quad) is also an outside chance of returning against Port Adelaide after the Swans' bye.
Longmire has also allayed fears over Rhyce Shaw's injury troubles, despite the running defender being listed as "indefinite" on the Swans' latest injury list.
Shaw has been suffering complications related to an abdominal tear, keeping him sidelined since round two.
But his coach says he has improved over the last week and should be able to return later in the season.
