Mumford appeared to be on a limited training schedule during Thursday's session at the SCG before media were locked out and he subsequently pulled up with groin soreness afterwards.
The 26-year-old had played every game this season, averaging 25 hit-outs and 3.5 tackles, and had formed a dangerous tandem with Mike Pyke.
Mumford's withdrawal could open the door for Jesse White to play his first match for the club since round seven last year.
Playing predominantly as a ruckman, White has been performing well in the reserves and would be the most likely replacement, with another back-up ruck option in Lewis Roberts-Thomson also injured.
White, 25, has managed 56 appearances in his five seasons at the Swans, including 20 in 2010.
Premiership winner Mitch Morton and Irishman Tommy Walsh are the other emergencies in the running to replace Mumford.
Both the Swans and Hawks carry 5-1 records into the Grand Final rematch at the MCG.
James Dampney is a reporter for AFL.com.au. Follow him on Twitter: @AFL_JD
