Aston Villa have today announced this. The condition was diagnosed following tests after the Bulgaria international, 32, developed a fever following last Saturday's defeat to Arsenal.
A club statement said: "We expect to learn more about Stiliyan's situation in due course and we have moved quickly to support him and his family.
"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.
"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."
Petrov's former Celtic team-mate and current Hoops manager Neil Lennon revealed his "absolute devastation" at the news.
Petrov spent seven years and won four Scottish Premier League titles at the Glasgow giants.
Lennon tweeted: "Absolutely inconsolable here regarding Stiliyan. He will overcome this like all the other barriers he faced in his life."
In a statement on Celtic's website, Lennon said: "We are all absolutely devastated to hear this news. As a member of the Celtic family, it is important for Stiliyan to know that he has our unequivocal support in battling against this disease.
"Knowing Stiliyan as I do, and the many obstacles he has overcome in his life to get to the peak of his career, he will overcome this one too.
"On behalf of the players and the backroom staff we send our support and best wishes to Stiliyan, Paulina and the family. We are there for them all and they will never walk alone."
The statement added that Lennon's coaching staff of Alan Thompson and Johan Mjallby, both former team-mates of Petrov as well, had both been left "stunned" by the news.
Celtic chief executive Peter Lawwell added: "This is terrible news and our support and prayers go to Stiliyan, Paulina and their family at this very difficult time.
"Stiliyan was an exceptional player for Celtic and helped to bring incredible success here during the seven years he spent at the club.
"He was also one of the most popular players here, not only within the club but with all our supporters and I know that they, too will want to pass on their support and best wishes to Stiliyan and his family."
Petrov - affectionately known as 'Stan' - was signed for Celtic by John Barnes.
He was handed the Villa captaincy by former manager Martin O'Neill, under whom he had previously excelled at Celtic.
The Bulgaria skipper took time to win over the Villa fans upon his arrival in 2006, before establishing himself as a key figure under O'Neill and his successors Gerard Houllier and current boss McLeish.