Gunmen rammed the last car in the ambassador's convoy as it was leaving a Tripoli hotel and robbed the occupants, the Libya Herald reported Wednesday.
The three-car convoy was exiting the Corinthia Hotel to take the ambassador to her residence in Palm City when the gunmen attacked.
Authorities said Apostolova was in an armored vehicle in the middle of the convoy ahead of the car that was rammed.
The incident took place Tuesday afternoon.
Witnesses said a police vehicle drove up during the attack but did not get involved.
In a related development, Libya's interior ministry is investigating an attack on a car carrying a diplomat from the Congo. His driver was slightly injured when armed men tried to steal the car in the Janzour area of Tripoli.
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