Stokes' father Ged, a former rugby league player, fell seriously ill on England's tour of South Africa at Christmas and has been unwell since.
His son has since paid emotional tribute to him when scoring centuries in Port Elizabeth and Old Trafford.
Stokes’ parents Ged and Deb live in Christchurch, where Ben was born before the family moved to Cockermouth in Cumbria.
The ECB said that Stokes would leave the bio-secure bubble as it moves back to the Ageas Bowl ahead of Thursday’s second Test, and will return to Christchurch this week, missing the remainder of the series.
The family have called for their privacy to be respected.
England took a 1-0 lead in the series on Saturday, with Jos Buttler and Chris Woakes taking them to an unforgettable come-from-behind victory.
Buttler did so after his father was admitted to hospital on Friday night.
Vice-captain Stokes, who has played the last two Tests largely as a batsman, will leave a huge hole in England’s team.
He is likely to be replaced by batsman Zak Crawley, but there are also likely to be other changes to the XI that won at Old Trafford as they manage bowlers’ workloads.
One complication is that Mark Wood, who has not played since the first Test of the summer, is a doubt with a niggle, so Sam Curran and the uncapped Ollie Robinson will come into contention.