The officials declined to give the name or nationality of the woman whom they described as one of his wives. The Lebanese newspaper As-Safir reported the army had detained her in coordination with "foreign intelligence apparatus".
The arrest is a blow to Baghdadi and could be used as a bargaining chip against his group which has captured many foreign, Iraqi and Syrian prisoners and declared a caliphate across territory his group seized in Syria and Iraq.
A senior Lebanese security official said Baghdadi's wife had been traveling with one of their daughters, contradicting earlier reports that it was his son. DNA tests were conducted to verify it was Baghdadi's child, the official said.
They were detained in northern Lebanon. Investigators were questioning her at the headquarters of the Lebanese defense ministry, the security officials said.
There was no immediate reaction from Islamic State websites to the arrest.
Islamic State has seized wide areas of Iraq and Syria, Lebanon's neighbor to the east.
The Lebanese security forces have waged a crackdown on Islamic State sympathizers in Lebanon and the intelligence services have been extra vigilant on the borders with Syria.
They have arrested over the past few months a number of Islamic militants suspected of staging attacks to expand Islamic State influence in the country neighboring Syria.
A U.S.-led alliance is seeking to roll back Islamic State's territorial gains in Iraq and Syria. U.S. President Barack Obama has vowed to "degrade and ultimately destroy" Baghdadi's group, which is seeking to reshape the Middle East according to its radical vision of Islam.
Spillover from the Syrian conflict has repeatedly jolted Lebanon. Militants affiliated to the al Qaeda-linked Nusra Front and Islamic State are demanding the release of Islamists held by the Lebanese authorities in exchange for 27 members of the Lebanese security forces taken captive in August.
Baghdadi, an Iraqi, called for attacks against the rulers of Saudi Arabia in a speech purported to be in his name last month.
He said his self-declared caliphate was expanding in Saudi Arabia and four other Arab countries and called for "volcanoes of jihad" the world over in the speech released on Nov. 13.
A CV of Baghdadi published on social media in July by Islamic State sympathizers described him as married but gave no further details. It is unclear how many wives he has. He is allowed up to four, in accordance with Islamic law.