Tottenham star Defoe, who only touched down in Poland with his England team-mates on Wednesday, will rejoin the squad at an unspecified date, the FA said in a brief statement.
"England striker Jermain Defoe has returned home to England this morning following the passing of his father overnight," the FA said.
"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."
Defoe is regarded as England's reserve striker, with Danny Welbeck and Andy Carroll vying for a starting berth against France next Monday in Group D in the absence of the suspended Wayne Rooney.