But the wicket-keeper is vowing to play on in the fifth and final Test against Australia in Sydney.
Stewart had medical tests before the start of play which confirmed he had contracted the virus.
Stewart was still able to take his place in the match, finishing the opening day unbeaten on 20 off just 13 balls, as England closed on 264-5.
He had only been declared fit enough to play a day earlier after recovering from a hand injury, which had threatened to end his participation in the final Ashes Test.
Stewart's team-mate Mark Butcher said: "We heard just before we got on the coach this morning that he thinks he's got chicken pox. He actually has got chicken pox.
"I think everybody has pretty well had it [chicken pox] before.
"But Alec wasn't feeling too good today."
If he was unable to continue in the match, Stewart could be replaced by wicket-keeper James Foster - but only if Australian captain Steve Waugh agrees to the specialist fielding change.
Australian team coach John Buchanan, asked whether he would have any objections to Foster coming in said: "I suspect not, but it would be up to Steve Waugh."
Many pundits are predicting the Sydney match, Stewart's 126th Test, could be his last.