The Welshman has pulled out to give himself the best chance of recovering from a slight injury in time to defend his 400m hurdles World title.
Greene's manager Jamie Baulch said: "In order for Dai to compete at the Sainsbury’s Anniversary Games he pulled out of Monaco, this gave him the good chance of recovering from a slight niggle in his leg.
"Unfortunately though, after a week in training a decision has been made between Dai and Malcolm (his coach) not to compete in London.
“Dai now has three weeks recovery time, this will hopefully be the time that Dai needs to ensure that he is on the plane to Moscow to defend his World title.”
800m runners Andrew Osagie and Jessica Judd have also withdrawn as a precaution ahead of the World Championships in Moscow that start in just over two weeks.
Osagie is still recovering from a hamstring problem whilst Judd has a small niggle in her calf.
Osagie said: "I am gutted to have to miss the race on Friday. It would have been amazing to be back in the Olympic Stadium.
"I hurt my hamstring in the 800m in Lausanne a few weeks ago and it kept me out of the trials. I'm recovering well and am back in full training, but I'm just not ready to race. I'll definitely be ok for Moscow though which is good news."