No immediate replacement will be called up for the Everton centre back, the FA added.
The 34-year-old, who has 39 international caps, will be the third player to pull out from the initial England squad for the qualifiers, following the withdrawals of Glen Johnson and Raheem Sterling.
England host Malta at Wembley Stadium on Saturday before travelling to take on Slovenia three days later.
England enjoyed a last-gasp 1-0 victory away to Slovakia in their opening Group F game last month. The group also includes Scotland and Lithuania.
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(Reporting by Nivedita Shankar in Bengaluru; Editing by John O'Brien)
