The woman was identified as Saja al-Dulaimi, an Iraqi, by a Lebanese security official and a senior political source.
The Lebanese newspaper As-Safir reported she had been detained in coordination with "foreign intelligence".
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 in territory it has seized in Syria and Iraq.
A senior Lebanese security official said Baghdadi's wife had been travelling 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 Lebanese defence ministry. There was no immediate reaction from Islamic State websites.
Dulaimi was one of 150 women released from a Syrian government jail in March as part of a prisoner swap that led to the release of 13 nuns taken captive by al Qaeda-linked militants in Syria, according to media reports at the time.
A source with contacts with Iraqi intelligence said the captured woman was an Iraqi wife of Baghdadi’s, but could not confirm the name. There was cooperation between Iraqi and Lebanese authorities leading up to her capture, the source said.
Baghdadi has three wives, two Iraqis and one Syrian, according to tribal sources in Iraq.
Islamic State has seized wide areas of Iraq and Syria, Lebanon's neighbour to the east.
The Lebanese security forces have cracked down on the group's sympathisers and the intelligence services have been extra vigilant on the borders with Syria.    
They have arrested over the past few months dozens of Islamic militants suspected of staging attacks to expand Islamic State influence in Lebanon.   
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.

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