Richards will now miss the FA Cup semi-final against Manchester United on April 16 as well as the bulk of City's matches in the title run-in after a scan revealed a grade two muscle tear.
"It is not what I wanted to hear at all. 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," Richards said on Manchester City's website.
"All I can do now is concentrate on getting back as quickly as possible. I must admit I did think 'why me?' for a while when I heard the news.
"Of all the games to miss, a Wembley date with United is the last one any player would choose."