Ben Stokes did not train with England on Tuesday because his father had been admitted to hospital in South Africa after suffering a serious illness.
Stokes’ father, Ged, was in a critical condition after being taken to hospital in Johannesburg on Monday.
All-rounder Stokes, 28, did not attend England’s training session at SuperSport Park so he can be at his 64-year-old father’s bedside.
“It puts things in perspective,” said England captain Joe Root.
“We’re here to play good, hard cricket, but it’s important as a squad that we want Ben and his family to have all the support they can get.”
Root said he did not know whether Stokes would be available for the first of four Tests against South Africa, which begins on Thursday (08:00 GMT).
“What’s most important is we support him and his family. It’s crucial that comes first,” he added.
Meanwhile, all-rounder Chris Woakes is the latest player to miss training because of illness in the England camp.
Bowlers Jofra Archer, Stuart Broad and Jack Leach all missed the warm-up matches but have returned to training.
“We’re trying to manage it as best we can,” said Root.
“We have some very talented players who, given an opportunity, will be desperate to prove a point and stand their mark on this series.
“We will probably have to pick a side at the last minute.”
England’s leading Test wicket-taker James Anderson, 37, is set to feature against South Africa in what will be his 150th Test appearance.
“It’s a phenomenal achievement – but to do it as a fast bowler, putting your body through that for that amount of time, shows incredible stamina,” said Root.
“He physically looks in as good a shape as I have ever seen him. He is a great example to any young player and the rest of our squad.”