Rich has been limited in training for a number of weeks but managed to play through - until Saturday night's loss to Fremantle, after which he pulled up sore.
The 21-year-old has played 59 consecutive matches since making his debut against West Coast in round one, 2009.
Lions physical performance manager Brett Burton said the injury had been lingering for a little while and would force him out of Sunday's match against Port Adelaide at the Gabba.
"'Richy’s' been having an issue with his foot for the past few weeks," Burton said.
"It’s a stress reaction. We’ve been monitoring and modifying his training loads, but unfortunately the injury has gotten worse so he’s now unavailable for the next couple of weeks."
The injury to Rich is the latest chapter in a horror season for the Lions with injuries.
He joins vice-captains Mitch Clark (ankle), Daniel Merrett (back) and Josh Drummond (knee) on the sidelines, while small forward Todd Banfield (hamstring) is still watching from the stands.
The Lions have received some good news ahead of Sunday's match though, with Jed Adcock back from a broken finger, and Brent Staker available after 14 weeks on the sidelines following injury to his anterior cruciate ligament in round one.
Rich has been an iron man for the Lions since being taken at No.7 in the 2008 National Draft from Subiaco in Western Australia.
He had a stellar first season and won the NAB Rising Star award in a unanimous decision.
He has finished top-10 in the club's best and fairest awards in both of his seasons and has put together another solid season in 2011 so far, including a 14 disposal, two goal performance at Patersons Stadium last Saturday night.
