"Military intelligence detained one of his wives, who was travelling with their son, near (Lebanese border town) Arsal 10 days ago," a security source told AFP.
A military source confirmed the arrest and said the woman was a Syrian national, and her son was around eight years old.
Lebanese daily As Safir, which first reported the arrest, said it was carried out "in coordination with foreign intelligence agencies".
The security source said the wife and child were taken to the defence ministry headquarters in Yarze "where investigations were continuing."
The security source said the arrest had been kept secret while security arrangements were made.
Baghdadi was proclaimed "caliph" of IS's self-declared Islamic "caliphate" spanning territory in Syria and Iraq in June.
He was put on the US "terrorism" watchlist in October 2011, and there is a $10 million (eight million euro) bounty for his capture.
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