The Football Association confirmed the news on Thursday morning, adding that the player is expected to return at some point and no replacement is being called up.
It is not known at this point whether Defoe will be back prior to Monday's Group D opener against France in Donetsk.
"England striker Jermain Defoe has returned home to England this morning following the passing of his father overnight," read an FA statement.
"Jermain will re-join the England Euro squad in due course. There will be no replacement player called in.
"We would ask all media to respect Jermain and his family's privacy at this difficult time."
Tottenham have also offered their sympathies to Defoe. "Everyone at the club sends their sincere condolences to Jermain and his family," the Premier League club said.
The Football Association and England manager Roy Hodgson will offer Defoe as much time off as he needs and still view the 29-year-old as a central component of the squad, even though he was unlikely to start against France.
It was Defoe whose goal against Slovenia in the last World Cup propelled England into the knockout phase, although he has been a peripheral figure for much of the European Championship qualifying campaign after scoring a hat-trick in the win over Bulgaria in September 2010.
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