The 38-year-old world record-holder had to pull out after a foot problem flared up again.
UK Athletics said in a statement: 'After a fitness test on Sunday it was concluded that she would not be able to race competitively to the best of her abilities.'
Radcliffe said: 'From the day when it was announced that London had won the bid, taking part and performing well in the London Olympic Games has been a major goal in my life.
'The goal of a fifth Olympics in my home country, what better? The chance to make amends to myself for bitter disappointments at the previous two Olympics.
'Through a lot of tough times it has kept me fighting, motivated and focused. That is why it hurts so much to finally admit to myself that it isn't going to happen.
It can break your heart and spirit many times over when your body is simply unable to match what your heart and brain want it to doPaula Radcliffe
'My sport is a beautiful sport, it gives so much fun and enjoyment, I believe it helps me to be a better person, and I have been very fortunate to experience some great success and have so many beautiful and happy memories.
'However, the downside is that it can break your heart and spirit many times over when your body is simply unable to match what your heart and brain want it to do.'