The bomber detonated explosives at a checkpoint near Camp Chapman, formerly used by the CIA, in eastern Khost province on Sunday.
Camp Chapman was the site of one of the worst attacks on the agency in 2009 when a bomber killed seven officials.
No US or coalition soldiers were killed in this latest attack.
The base now houses both Afghan and foreign troops, including US soldiers.
Youqib Khan, the deputy police chief in Khost province, told the Associated Press news agency that Sunday's blast hit a checkpoint manned by members of an Afghan unit that guards Camp Chapman.
Officials said those killed were civilians in cars waiting to clear the checkpoint at the time of the blast.
No group has said it carried out the blast as yet, although the Taliban has often targeted troops and launched a fresh offensive in late April.
Khost borders Pakistan and is one of Afghanistan's most volatile provinces.

The government has put aside 10bn roubles ($272m; Â£164m) to pay owners of cars that are at least six-years old an incentive to buy a new vehicle.
Car owners will be eligible for a discount of at least 40,000 roubles.
The government expects the scheme, which will run to the end of the year, to subsidise the sale of more than 170,000 vehicles.
The scheme could "seriously stimulate sales," said Prime Minister Dmitry Medvedev, according to local news agencies.
Car sales fell by almost a quarter in July compared with a year earlier, following a sharp fall in the previous month.
Russia, along with many other countries including the US, the UK, Germany and France, first introduced a car scrappage scheme during the global economic downturn.
A suicide car bomb has killed at least 17 people, mostly women and children, near a military base in Afghanistan, officials say.
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Russia has said it will introduce a new scrappage scheme to try to boost flagging car sales.