It was initially reported that a wife and son of the self-proclaimed "caliph" had been arrested last month. The woman, who has been named as Saja al-Dulaimi, was travelling with two sons and a daughter, Interior Minister Nouhad Mashnuq told the Lebanese MTV channel late Wednesday.
He said DNA tests showed that the girl was Baghdadi's child.
"Dulaimi is not Abu Bakr al-Baghdadi's wife currently. She has been married three times: first to a man from the former Iraqi regime, with whom she had two sons," he said.
"Six years ago she married Abu Bakr al-Baghdadi for three months, and she had a daughter with him. Now, she is married to a Palestinian and she is pregnant with his child," Mashnuq added.
"We conducted DNA tests on her and the daughter, which showed she was the mother of the girl, and that the girl is his (Baghdadi's) daughter, based on DNA from Baghdadi from Iraq," the minister said.
He gave no details on Dulaimi's nationality, but a security source said she was believed to be Iraqi.
Mashnuq offered no further information about her current husband, although he said investigations showed the woman had ties to extremists in Lebanon.
Dulaimi's children were at a children's care centre while she was being interrogated, he said.
Mashnuq also confirmed the arrest of the wife of Anas Sharkas, a leader in Al-Qaeda's Syrian affiliate Al-Nusra Front.
Dulaimi was among a group of female prisoners released from Syrian jails in March, in exchange for 13 nuns from the ancient town of Maalula held by Al-Qaeda's Syrian affiliate Al-Nusra Front.
The ISIS group has yet to comment publicly on Dulaimi's detention, but Al-Nusra, despite a feud with Baghdadi's group, issued a statement of condemnation.
It described her as "sister Saja al-Dulaimi" and said the arrest of women and children was evidence of the "weakness" of the Lebanese state.
Sources said the detention of Dulaimi and Sharkas's wife could help the Lebanese as they struggle to negotiate the release of 27 members of the security forces held by terrorists from “IS” and Al-Nusra.
The soldiers and police were abducted when militants from the two groups briefly overran the Lebanese border town of Arsal in August.
The fighters withdrew after a truce negotiated by clerics, but took 30 hostages, three of whom have been executed.
Later Iraq's Interior Ministry said on Wednesday that a woman detained by Lebanese authorities was not the wife of ISIS leader Abu Bakr al-Baghdadi, but the sister of a man convicted of bombings in southern Iraq.
Ministry spokesman Brigadier General Saad Maan told “Baghdadi had two wives, but "there is no wife in the name of Saja al-Dulaimi”.