His decision comes in the wake of media allegations that John Terry, his former Chelsea team-mate who is also in the England squad, had an extra-marital affair with Bridge's former girlfriend.
Bridge was a club mate of Terry's at Chelsea before joining Manchester City last year.
In the statement, issued to Sky Sports News, Bridge said: "I have thought long and hard about my position in the England football team in the light of the reporting of the events over the last few weeks.
"It has always been an honour to play for England. However, after careful thought I believe my position in the squad is now untenable and potentially divisive.
"Sadly therefore, I feel, for the sake of the team, and in order to avoid what will be inevitable distractions, I have decided not to put myself forward for selection.
"I have today informed the management of this decision. I wish the team all the very best in South Africa."
His decision leaves England coach Fabio Capello with a problem at left back as Ashley Cole, another former Chelsea team mate of Bridge's, is out until May at the earliest.
"I was flying when Bridge announced that he would not stay with us for the next game against Egypt, also for the future, in the World Cup, and that surprised me ..." said Capello.
"I respect the decision of the players but the door for him (Bridge) is always open," added Capello.
"We have time, three months, before my last squad for the World Cup. I hope that Wayne Bridge will be with us at the World Cup but I respect the decision of the player."
