White, who has four England caps, has been dealing with a hamstring problem and missed Arsenal’s last Premier League game of the season against Everton.
The centre-back was still selected by England boss Gareth Southgate ahead of next month’s Nations League games.
But he will now stay at Arsenal for treatment as he looks to return in time for next season.
Raheem Sterling, Kieran Trippier and James Ward-Prowse will arrive at England’s St George’s Park base on Tuesday, along with Trent Alexander-Arnold following Liverpool’s Champions League final defeat against Real Madrid.
England face a double header against Hungary and games against Germany and Italy as they start their Nations League campaign ahead of the World Cup in Qatar later this year.