The mother and a four-member Channel Nine crew have been detained in Beirut since last Wednesday, judicial sources said, after authorities scuppered their attempt to take the woman's two children back to Australia.
CCTV footage broadcast on Lebanese television appeared to show several people grabbing the children, who the father said were aged five and three, from their grandmother and bundling them into a car.
The mother was subsequently arrested and the children were returned to their father.
Channel Nine said its crew was not connected to the people who grabbed the children, Australian media reported.
The files on the case have been transferred to a judge for further investigation.
Lebanon, unlike Australia, is not a signatory of the Hague Convention on the Civil Aspects of International Child Abduction, which allows for children normally resident in one location to be returned if taken by a relative.
Australian Foreign Minister Julie Bishop said on Saturday she could not "understate the seriousness with which the Lebanese authorities are viewing the case" and added that Canberra was handling it "very carefully".