White has returned to England and is not expected to return to the squad until after the conclusion of the Qatar 2022 FIFA World Cup.
White has been an unused substitute in all of England's three group stage games.
The 25-year-old, who was also an unused substitute in all England games at last summer's European championships, has four caps for his country.
A statement released by the Football Association on Wednesday read: "Ben White has left England's training base in Al Wakrah and returned home for personal reasons.
"The Arsenal defender is not expected to return to the squad for the remainder of the tournament.
"We ask that the player's privacy is respected at this moment in time."
England topped their group with two wins and a draw, and will face Senegal in the round of 16 on Sunday.
White has been in good form for Arsenal this season, playing prominently at right back and helping Mikel Arteta's side to the top of the Premier League table.
