Powell was due to take on American rival Tyson Gay over 100 metres on Friday, but has a groin strain.
Powell says he has been "carrying some soreness in my groin since the Olympic trials and have been unable to train at 100 per cent."
In a statement from London GP organizers, he added: "I need to ensure I'm ready for the games and cannot take any risks. I will be ready in August."
The Olympics start on July 27.
But Powell also missed last year's London Diamond League meeting with a groin injury, which led to him missing the world championships in August.