Rose was added to Roy Hodgson's party for the Euro 2016 qualifier against Lithuania and a friendly against Italy when Manchester United's Luke Shaw pulled out.
"The left back will play no further part in preparation for the forthcoming fixtures against Lithuania and Italy and has returned to his club," the FA said in a statement on Wednesday.
Rose has pulled out with hip and hamstring injuries, according to media reports.
England have already suffered a number of injury withdrawals. Liverpool pair Daniel Sturridge (hip) and Adam Lallana (groin) pulled out after their team lost to Manchester United in the Premier League on Sunday.
Southampton goalkeeper Fraser Forster dropped out after suffering a season-ending knee injury following Saturday's win over Burnley.
England, who top Group E with four wins from four matches, host Lithuania at Wembley on Friday before meeting Italy in a friendly in Turin four days later.
(Reporting by Toby Davis, editing by Tony Jimenez)
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