Conca, one of the Tigers' best so far this season, has been diagnosed with a stress reaction, says the club.
"The good thing is we picked it up this early. It didn't develop into a crack or stress fracture," Richmond's elite performance manager Peter Burge told the club's website.
Conca will be placed in a moon-boot initially before he returns to running.
He has definitely been ruled out of the Tigers' clash with Fremantle in Perth on Friday night, and most likely the following three games.
