"It is likely that he will miss four to six weeks of action though he is determined to press ahead with plans for an oxygen tent in his house in a bid to speed his recovery," City said on their website.
Richards, who suffered the injury playing for the England under-21 side last week, will miss the FA Cup semi-final against Manchester United on April 16, as well as most of the Premier League run-in.
"It is not what I wanted to hear at all," Richards said after a hospital scan revealed a Grade Two tear in his hamstring.
"I felt sick when I was told. I knew from experience when I did it that it felt like a bad one but I was hoping for the best."
City are to seek a second opinion on the knee injury suffered by defender Jerome Boateng while training with the German national team.
"Initial reports from the German camp suggested Boateng will need surgery but the Blues will seek a second opinion once the club's own medical staff has made an assessment," City said.
Manager Roberto Mancini's options in defence have been further hit with Pablo Zabaleta away on compassionate leave in Argentina.
With Kolo Toure suspended, Mancini is considering calling up youngsters Dedryck Boyata and Wabara Reece to face Sunderland on Sunday.
