Bridge said in a statement that his presence in the World Cup squad could cause friction, leaving coach Fabio Capello with potential problems filling the left back position.
First-choice left back Ashley Cole is already questionable for England's opening match against the United States on June 12 after sustaining an ankle injury.
The 29-year-old Bridge announced his decision despite Capello predicting earlier this week that the defender would be capable of playing in the same team as Terry, who was stripped of his captaincy when details of the alleged affair emerged.
"I have thought long and hard about my position in the England football team in the light of the reporting and events over the last few weeks," Bridge said in a statement Thursday. "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."
