Flintoff injured his left foot in the third Test win over New Zealand earlier this month.
"He has been advised to rest for two weeks. Scans show no serious damage," an England and Wales Cricket Board (ECB) said on Wednesday.
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added the priority would be to get Flintoff fit for the four Tests against West Indies starting next month.
England play New Zealand in the first match of the ten-game tournament at Old Trafford on Thursday. The final takes place at Lord's on July 10.
Surrey all rounder Rikki Clarke has already been brought into the squad to cover for Flintoff. Glamorgan batsman Michael Powell has also been called up after opener Marcus Trescothick twisted an ankle.
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