The move was announced by the British Olympic Association after it was revealed the 30-year-old, who was selected alongside fellow marathon runners Scott Overall and Lee Merrien, did not pass a fitness test.
Leeds-based Webb was struggling to make the Games with a stress fracture.
Dr Ian McCurdie, the BOA’s chief medical officer, in conjunction with Team GB Chef de Mission Andy Hunt, advised on the withdrawal from the team on medical grounds.
Hunt said: “We wish Dave the very best in his recovery and applaud him for offering his continued and full support to his athletics teammates.”
The BOA will not be nominating a replacement.