Richards suffered the problem on Olympic duty with Team GB and City manager Roberto Mancini expected him to recover in time for Sunday's Barclays Premier League encounter with Southampton, but the 24-year-old's recovery has not gone quite as well as planned.
"I think it will be three or four more weeks," said Mancini.
Mancini also confirmed Gareth Barry remains on the sidelines with an abdominal problem.
However, Joe Hart could be fit after missing both the Community Shield and England's win over Italy with a back problem.
"Joe will train with the team tomorrow, then we will decide," added Mancini.
Source: PA
Source: PA