The 49-year-old Jimmy Defoe is thought to have been ill for some time.
The Spurs frontman is now likely to miss Monday’s opener against France, with the FA announcing that Defoe will re-join the squad "in due course", with no plans to call-up a replacement player.
The statement on the governing body’s official website read: "England striker Jermain Defoe has returned home to England this morning following the passing of his father overnight.
"Jermain will re-join the England Euro squad in due course. There will be no replacement player called in."
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Defoe arrived in Poland with the rest of Roy Hodgson's squad on Wednesday to start their competition preparations.
Tottenham have released their own statement on their official website, also passing on their condolences: "Everyone at the Club sends their sincere condolences to Jermain and his family."
The 29-year-old has won 47 senior 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, scoring the only goal of the game against Slovenia to secure England’s progression to the knockout round.
Defoe played 23 minutes as a substitute in England's final pre-Euro 2012 friendly against Belgium at Wembley on Saturday.