Over the weekend the ban was established by the Tobruk government's military chief-of-staff Abdul Razzaq al-Naduri - an ally of military strongman Khalifa Haftar - who has defended the ruling in the face of growing criticism claiming the measure was taken for "security reasons".
A number of Libyan women travelling outside the country have been in contact with foreign intelligence agencies, he claimed, saying the travel ban had nothing to do with religious precedents.
According to the ruling, women under 60 attempting to leave the country from the eastern Labraq airport can only do so with a male guardian.
The Tripoli-based "national unity" government, which is recognised by the UN, has not enforced any such ruling in territory it controls. The ruling, which echoes state-imposed legislation in Saudi Arabia, has been viewed as evidence of growing political divides in Libya that have effectively split the country in two, with each side enforcing their own set of rules.
On Monday, local media reported that a convoy carrying the head of the Tripoli-based government, Fayez al-Sarraj, came under fire in the capital. No casualties were reported.
Despite divisions, last week the Tripoli and Tobruk-based governments agreed in Cairo to hold unified presidential elections by February 2018.
Since the travel ban was announced, Libyans have taken to Twitter to express criticism, with one Libyan comedian based in Jordan even recording a song mocking the ruling - over the Enrique Iglesias hit Hero, he sings "I can be your muhrim baby."