Defender stretchered off early in victory over Denmark and could miss games FA Cup semi-final against Manchester United as well as league games against Liverpool and Sunderland
The full-back managed only a few minutes on the pitch before being stretchered off with the problem during the friendly in Viborg and was replaced by James Tomkins.
Richard's injury has yet to be fully assessed and will go under the eye of specialists over the next few days, however, international boss Stuart Pearce has revealed that the player himself expects to be out for a month.
"He's got a hamstring problem and he's diagnosed himself as being out for four weeks - that's Dr Richards for you," said Pearce.
"That could be four days though, as that's him diagnosing himself!
"Let's hope for Manchester City's sake and the preparation in the summer that it's not too long."
An absence of such a period would have the 22-year-old miss vital games for City in the race for fourth, as well as the FA Cup semi-final against local rivals Manchester United at Wembley.