"Andrew's ankle did not demonstrate sufficient improvement after his first bowling session today," a statement from the England and Wales Cricket Board said Wednesday.
The second match in the four-test series starts Friday at Headingley in Leeds.
Flintoff has had two operations on his left ankle in the past three years. He was out for most of England's summer last year with an ankle injury, returning as captain for the limited-overs ICC Champions Trophy and the ensuing 5-0 Ashes test series defeat in Australia.
England and West Indies drew the first test at Lord's.
Russia has left the list of 33 largest holders of US government bonds, after the country disposed of at least a third of remaining bonds