A security source said the homemade bomb, locally known as "gelatina", had been placed near a car on a street in the central district of Dahra where the three embassies are located.
The car, parked outside the Greek embassy, was slightly damaged and there were no reports of casualties.
On April 23, a car bomb detonated outside the French embassy in the upmarket Gargaresh area of Tripoli, causing extensive damage and wounding two embassy guards and several local residents.
"A bomb was thrown from a car at an army checkpoint at the Dubail crossroads in the centre of Benghazi," a security official said, speaking on condition of anonymity.
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Benghazi, cradle of the 2011 uprising against former dictator Muammar Gaddafi, has seen a spate of attacks on security forces and Western interests in recent months.
The latest bombings highlight the inability of authorities to establish effective security in Libya, which has been awash since the uprising with weapons used by former rebels and other groups who helped topple Gaddafi's regime.
Yesterday, a bomb apparently targeting troops guarding an empty Benghazi school building caused damage but no casualties.