Richards suffered the problem on Olympic duty and Blues manager Roberto Mancini expected him to recover in time for Sunday's Barclays Premier League encounter with Southampton.
However, 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 [Saturday], then we will decide," said Mancini.
Mancini was accompanied at his scheduled pre-match briefing by new signing Jack Rodwell, who expressed his determination to meet the challenge provided by the additional pressure of his move from Everton.
However, it was another new arrival that has been the talk of Manchester over the past 24 hours as Robin van Persie looks to tie up his move to United from Arsenal.
And the City manager is certain the Dutchman will improve his major rivals.
"Robin van Persie is a really top player and the best striker last year," he said.
"With Wayne Rooney they will have one of the best couple of strikers in the Premier League.
"Any team that bought Van Persie would be better and I was serious last week when I said Manchester United were the favourites.
"They have been playing for the title every year for 20 years. We can't change this situation in one year."
It was felt Mancini wanted to sign Van Persie himself, however, he claimed it was not a realistic possibility.
"I felt he was going to stay at Arsenal or sign for another team, but not us," he said.
"We already have four strikers. It was impossible for us to sign another one."