Hamid Albandag, a member of the internationally recognised parliament, says the early today airstrike hit near a hospital. It was not immediately clear who carried out the strike.
Darna is controlled by an alliance of Islamic militant groups which have been defending the town from Islamic State militants. Albandag says the IS group is 6-7 kilometers outside the city.
Libya has fallen into chaos since the 2011 toppling of longtime dictator, Moammar Gadhafi.