Bale was set to be named in Stuart Pearce's GB 18-man squad, which is announced on Monday.
It is understood the 22-year-old Wales international has suffered a recurrence of an old back and hip injury after pulling up while running.
Bale is understood to be reluctant to risk aggravating the problem further, with Tottenham's Premier League opener at Newcastle just seven weeks away.
The player, who earlier this week pledged his future to Spurs by signing a new four-year contract to 2016, is believed to have already informed Pearce of his decision to make himself unavailable for selection after taking medical advice.
The Welshman is the second big name to be ruled out this week. On Thursday, David Beckham revealed he had not been selected as one of three over-23 players permitted in the squad.
The Olympic tournament starts on July 26, with Great Britain drawn in a group with Uruguay, Senegal and the UAE.