The Tottenham striker will return to the Euro 2012 squad in due course, the FA confirmed in a brief statement, and as a result England manager Roy Hodgson will not call up a replacement.
Defoe's father died overnight on Wednesday.
England arrived at their base in Krakow, Poland yesterday, ahead of their opening game against France on Monday.
Whether Defoe would return in time for that fixture is unclear at this stage, but his absence would leave England with Andy Carroll and Danny Welbeck as their only fit and available strikers for the opener.
Defoe has 47 caps and 15 goals to his name for England.
"We would ask all media to respect Jermain and his family’s privacy at this difficult time," the FA added.
Spurs also extended their sympathies towards their striker, releasing a statement which read: "Everyone at the club sends their sincere condolences to Jermain and his family."