"We had earmarked the fourth and fifth matches as an opportunity to rest Graeme ... as we have to consider our preparations for the test series against South Africa [ Images ] later this month," said national selector Geoff Miller in a statement on Thursday.
"Graeme has some pain in his elbow at the moment and we feel an extra week's rest will allow it to settle."
Jade Dernbach is also to miss the remaining two matches with a side strain.
Pace bowler Chris Woakes, drafted in for the third one-dayer in Birmingham that was washed out on Wednesday, stays in the squad and off-spinner James Tredwell has been called up.
The fourth match is in Durham on Saturday. England lead the series 2-0.