"Four members of our force and two staff (at the passport department) were wounded in the attack targeting the department's headquarters," said special missions and counter-terrorism force patrol commander Hamdi al-Dinali.
He blamed "terrorist sleeper cells" in the eastern coastal city for the attack.
Libya has been rocked by chaos since a 2011 uprising that toppled and killed dictator Moamer Kadhafi, with two rival authorities and multiple militias vying for control of the oil-rich country.
Military strongman Khalifa Haftar in July announced the "total liberation" of Benghazi, three years after his forces launched a military operation to seize the city from jihadists.
Haftar supports a parliament based in the far east of Libya, while a rival UN-backed unity government in the western capital Tripoli has struggled to assert it authority nationwide.