The Tottenham striker has left the Three Lions base camp in Poland but will return "in due course," with no replacement call-up planned, according to the Football Association.
The FA has announced that Defoe will rejoin to the squad "in due course" and that there are no plans to call up a replacement player.
"Everyone at the Club sends their sincere condolences to Jermain and his family," a statement released by Tottenham read.
Defoe arrived in Poland with the rest of Roy Hodgson's squad on Wednesday ahead of their opening Euro 2012 fixture against France on Monday evening.
The 29-year-old has won 47 England caps, scoring 15 goals, but is yet to appear in a European Championship. He did feature as part of the Three Lions' 2010 World Cup squad in South Africa.
Defoe played 23 minutes as a substitute in England's final pre-Euro 2012 friendly against Belgium at Wembley on Saturday.
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