The German international is due to undergo further tests to determine the strain of meningitis and the prognosis in terms of his recovery," the club said on their website.
Stoke start the new season with a league game at promoted Reading on August 18 but manager Tony Pulis said that was of secondary concern.
"It's a massive, massive worry for us but the most important thing right now is Robert's health and we are keeping our fingers crossed he'll be okay," said Pulis.
"He started to feel unwell last week ... and then felt a lot worse over the weekend."
Huth, 27, has previously played for Chelsea and Middlesbrough, from where he joined Stoke for a £5 million fee in 2009.
In June this year he agreed a new deal with the club to keep him at the Britannia Stadium until the end of the 2015/16 season.
Meanwhile, Pulis has confirmed interest was building in trialist Sebastian Boenisch.
The Polish international left-back, who played in all of Poland's Euro 2012 matches, was released from Bundesliga outfit Werder Bremen and is looking to seal a move to the Premier League.
"Sebastian is available on a free transfer, so we're taking a look at him over the next couple of matches and we'll take it from there," Pulis said.