The self-styled Libyan National Army’s announcement comes two American and Italian unmanned drone aircraft lost near the capital last week.
Warlord Haftar's forces fighting for control of Libya's capital say they are imposing a "no-fly zone" there.
In a statement, the UN-recognised GNA Interior Ministry said any action threatening civil aviation and airports "amounts to crimes punishable under national and international law".
In April, warlord Haftar’s forces launched a military campaign to capture Tripoli from the internationally-recognised GNA, but have so far failed to make advance beyond the city's outskirts.
Since the ouster of late ruler Muammar Gaddafi in 2011, two seats of power have emerged in Libya, one being in eastern Libya supported mainly by Egypt and the United Arab Emirates, and another in Tripoli, which enjoys UN and international recognition.
The self-styled Libyan National Army’s announcement comes after two unmanned drone aircraft — one American and one Italian — were lost near the capital last week.
The LNA has said it shot down the Italian drone, while the US military hasn't given a reason for its drone’s loss.
Ahmed al-Mosmari, an LNA spokesman, said late on Saturday that all flights over Tripoli and nearby towns are "prohibited without prior coordination."