The attacker blew himself up in a car in front of the base in Barsis, some 50 km (30 miles) outside Benghazi, a security source said.
All those killed were soldiers, medical sources said, but the security source said the attacker was among those killed.
The security situation has sharply deteriorated in Libya’s second-largest city in the past few months where car bombs and assassinations of army and police officers happen regularly.
Most countries closed their consulates in Benghazi after a series of attacks and some foreign airlines have stopped flying there. The U.S. ambassador and three other Americans were killed in September 2012 during an Islamist assault on the consulate.
Separately, tribesmen in Jalo in the southeast brought the bodies of five soldiers to a local hospital, state news agency Lana said. The soldiers had been killed in clashes two days ago, the agency said without giving details.
Western diplomats worry the violence in Benghazi will spill over to the capital Tripoli which last month saw the worst fighting in months between militias.
Much of Libya’s oil wealth is located in the east where many demand autonomy from the Tripoli government, adding to turmoil in the North African country.
Oil exports, Libya’s lifeline, have fallen to 110,000 barrels a day, a fraction of the more than 1 million bpd in July as armed militias, tribesmen and minorities have seized oilfields and ports to press for political and financial demands.
Zeidan has warned the government will be unable to pay public salaries if the protests continue.