The Essex left-hander has been struggling with a right shoulder injury since England's victory in the final Test at Trent Bridge over a week ago.
He was ruled out of the Twenty20 international at Old Trafford and Sunday's resounding victory in the opening match of the series at Chester-le-Street.
Following further tests, Cook is still not fit and England have added Middlesex left-hander Andrew Strauss to the squad for the Edgbaston game as cover.
No laughing matter: England one-day skipper Paul Collingwood (left) and Graeme Swann (right) share a joke with Alistair Cook
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London gets ready for the Diamond Jubilee - in pictures
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Diamond Jubilee: Boat by boat, here is where to watch the Queen's Thames flotilla - VIDEO
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Duchess of Cambridge is pretty in pink at her first Buckingham Palace garden party
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News pictures of the day
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London 2012 Olympics: Raising the bar and the Games haven't even started yet. Price of toasting Team GB is £6 a pint! -
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