Robinson, 30, made his international debut in 2003 and became first-choice during the 2006 World Cup, but he was widely blamed for England's defeat against Croatia in qualification for Euro 2008 and he was later dropped by then England boss Steve McClaren.
Capello called Robinson into his squad last year for the 2010 World Cup qualifiers against Kazakhstan and Andorra, but he was unable to force his way into the side and was left out of the squad for South Africa in favour of David James, Robert Green and Joe Hart.
On Saturday night, Capello handed Robinson a recall for next week's friendly match, but the former Leeds and Tottenham 'keeper has taken the opportunity to announce that he has no interest in being a squad player for his country.
In a statement, he said: "I have taken the decision to retire from international football with immediate effect. Only now have I been able to make this decision because previously I have not been in contention or selected for the squad.
"As a professional who wants to play every time I have the chance, I don't see myself as a number three or four keeper and find that role very frustrating. I haven't had the opportunity of anything other than this in recent years.
"Therefore, I feel it's in the best interests of myself and my club, Blackburn Rovers, to concentrate solely on my club football. I wish the England team every success."
Blackburn boss Sam Allardyce has backed Robinson's decision to turn his back on England duty.
"For the time being, England will miss him," Allardyce said on Sunday. "They missed him at the World Cup because he should have gone there.
"He feels that if he isn't going to be number one, then he doesn't feel the need to be travelling with England. You'd have to ask him if he'd come back if guaranteed the number one spot, but I would presume so.
"Certainly at this moment in time, though, he doesn't feel that's the case. He feels that he should be number one and has always felt that way.
"As my player, I support him because I see him week in, week out and know how well he has performed. It's a big decision he's made, but I understand it.''
The FA has said Capello will not call up a replacement for Robinson, leaving Hart and Ben Foster battling for the chance to face Hungary.