The 32-year-old Bulgaria international has not trained since playing against Arsenal on Saturday.
The condition was diagnosed following tests after the midfielder developed a fever.
"The Villa board received news today that our long-standing captain Stiliyan Petrov has been diagnosed with acute leukaemia," the club said in a statement.
"Haematology experts confirmed the diagnosis today. We expect to learn more about Stiliyan's situation in due course. During this time we ask that Stiliyan's privacy is placed ahead of all inquiries.
"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."
Bulgaria's team doctor Mihail Iliev spoke to Darik Radio about the former CSKA Sofia man.
"Unfortunately, Stiliyan called me... to inform me about the illness," he said.
"It's very frustrating. He'll have exams tomorrow in London and we'll have more information after that. I personally hope that the illness is in the very early stages."
Petrov's illness is the second major health problem to have affected a Premier League player this month.
Bolton Wanderers midfielder Fabrice Muamba suffered a cardiac arrest on the pitch during an FA Cup game at Tottenham Hotspur two weeks ago but on Friday tweeted a picture of himself after a remarkable recovery.
"ABSOLUTELY INCONSOLABLE"
Villa are due to host Chelsea in the Premier League on Saturday and coach Alex McLeish said the game would go ahead according to Petrov's wishes.
"Put it this way, this is the first day of his recovery," McLeish told a news conference as he confirmed Petrov was already heading to London for tests.
"The players will be gutted but hopefully galvanised for the game for their captain."
Bolton postponed a match with Villa in the wake of Muamba's collapse.
Outside of England, it was announced earlier this month that Barcelona and France left-back Eric Abidal is to have a liver transplant.
Petrov, the most-capped Bulgaria international with 105 appearances, had great success as a player at Celtic before joining Villa and former team-mate Neil Lennon - now manager of the Scottish leaders - tweeted his sadness at the news.
"Absolutely inconsolable here regarding Stiliyan. He will overcome this like all the other barriers he faced in his life," he said.
"Stiliyan has the heart of a lion and as part of the Celtic family he deserves all our best wishes and support."
Other messages of support poured in from the football world.
Bulgaria coach Luboslav Penev missed the 1994 World Cup in the United States, when his side reached the semi-finals, as he had been diagnosed with testicular cancer.
"Let's keep calm and be patient until next week when there will be more clarity about Petrov's status," the former striker said.
"National team coaches and players are ready to help him with anything and we believe in his recovery."
