The condition was diagnosed following tests after the Bulgaria international, 32, developed a fever following Saturday’s 3-0 defeat at Arsenal.
It is understood Petrov will begin treatment in London on Monday.
In the meantime the former Celtic midfielder is being seen by medical specialists.
“We expect to learn more about the situation in due course,” a club statement continued.
“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.”
Petrov joined Villa from Celtic for £6.5m in 2006 and has scored 12 goals in 219 appearances.
He played the full 90 minutes at Emirates Stadium on Saturday, his 30th game of the season, but on the bus after the match he reported to a doctor that he felt unwell.
Aston Villa indicated on Wednesday that Petrov was feeling the affects of a virus, but news he was suffering from leukaemia was only confirmed earlier on Friday after medical tests.