The ban is said to be for "national security reasons" and not driven by religious ideology.
BBC North Africa correspondent Rana Jawad says it will affect all passengers transiting through the east.
Libya is divided between two authorities - one in the east and an internationally recognised one based in the capital, Tripoli.
The eastern government is based in al-Beyda and the ban was first enforced in the city's Labraq international airport.
The authorities in the east under the command of Gen Khalifa Hefter have control over an area stretching from Ajdabiya to Tobruk.
A spokesman for eastern Libya's Chief of Staff, Abdulrazzak al-Naduri, confirmed the new measure to the BBC.
In a TV interview, he claimed that women representing civil society groups, who frequently travel abroad for work, are being used by foreign intelligence.
The directive was not voted for by the parliament but it is already being implemented in the east.
Officers say it is to be enforced on travel by land, air and sea.
The restriction highlights the growing political divide in Libya, with each side enforcing its own rules in the area it controls, our correspondent says.
Libya has been beset by chaos since Nato-backed forces overthrew long-serving ruler Col Muammar Gaddafi in October 2011.
Eastern Libya is under the control of commander Khalifa Hafter who is leading the battle against Islamist militias.