A military official said the woman and child were detained about 10 days ago while carrying fake identification cards.
Both officials refused to give further details about the woman who is believed to be one of the wives of Abu Bakr al-Baghdadi, the group’s reclusive leader.
The officials spoke on condition of anonymity.
The military official said the woman is a Syrian citizen and is being questioned by authorities.
The announcement of the arrest comes amid attempts to reach a prisoner-exchange deal between Lebanese authorities on one side and on the other, the Islamic State group and the Nusra Front, al-Qaeda’s Syria branch, which have been holding more than 20 Lebanese soldiers and policemen hostage since August. They have demanded the release of Islamist prisoners being held by Lebanese authorities.
On Monday night, the Nusra Front threatened to kill one of the soldiers it holds captive.
The wife’s arrest could be used as a bargaining chip for Lebanese authorities in their attempts to win the freedom of the troops.
A judicial official said the interrogation is being supervised by Lebanon’s military prosecutor, Saqr Saqr. He added that a DNA test is underway to confirm that the child is the son of the detained woman.
The Lebanese daily As-Safir was the first to break the news, saying they were detained near a border crossing point with Syria. It added that the arrest was made in “co-ordination with foreign intelligence agencies.”
Very little is known about al-Baghdadi’s personal life, including how many wives and children he has. Conservative interpretations of Islam allow for a man to marry up to four wives.
Al-Baghdadi’s first wife is believed to be Iraqi citizen Saja al-Dulaimi, who was reportedly held by Syrian authorities and freed in a prisoner exchange with the Nusra Front earlier this year.
In March, the Nusra Front freed more than a dozen Greek Orthodox nuns, ending their four-month captivity in exchange for Syrian authorities releasing dozens of female prisoners.