Car bomb kills at least 13 in Shiite area of Baghdad
General Petraeus quit his post last week after acknowledging an affair with his biographer, Paula Broadwell.
A CIA spokesman says the inquiry by the agency's inspector general would see if there are lessons to be learned.
Mrs Broadwell, 40, was found to have classified information in her possession.
In his first interview since resigning, Gen Petraeus told CNN on Thursday he did not give any national security-sensitive information to his lover.
Petraeus denies passing secrets to mistress
In his first interview since resigning as CIA director last Friday over an extramarital affair, retired General David Petraeus said he did not share any classified documents with his mistress and biographer, Paula Broadwell.
Earlier reports said that that investigators had found substantial classified information on a computer used by Broadwell.
President Barack Obama said on Wednesday that there was no indication so far that any classified information had been disclosed as a result of the affair.
Voice of Russia, BBC, Reuters
