The condition was diagnosed following tests after the Bulgaria international, 32, developed a fever following Saturday's 3-0 defeat at Arsenal.
"We expect to learn more about the situation in due course," Villa said.
"Stiliyan is cherished by many and he will get from Villa every ounce of love and support that we have to help bring this to a positive conclusion."
A club statement added: "During this time we ask that Stiliyan's privacy is placed ahead of all inquiries and trust that we will share information as we receive it."
The former Celtic midfielder booked into a London hospital for immediate treatment on Friday.
Aston Villa manager Alex McLeish said Petrov was "defiant" and concerned about his loved ones.
He said: "He's on a train right now to go and get more tests, after the viral condition last week when he had a temperature.
"He reported to the doctor on the bus on the way back from the game. The doctor told me yesterday that we were still waiting on results.
"This is the first day of his recovery."
Of the other Villa players, McLeish added: "They are gutted but galvanised to try to win the game tomorrow for their captain."
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