The bomber detonated the explosives at a military roadblock near the entrance to Camp Chapman as people were rushing to get home for iftar, the meal breaking the Ramadan fast, said Faizullah Ghairat, the Khost city police chief.
There was no immediate claim of responsibility, but the Taliban has often targeted Afghan and foreign troops.
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However it is ordinary Afghans who are paying the price so far this year, the UN mission in the country has said.
Almost 1,000 civilians were killed during the first four months of this year, a sharp jump from the same period last year, the UN said.
"We counted 18 dead and six wounded," said a doctor at a hospital in Khost city today.
Ghairat put the toll at 25 dead and 16 wounded, adding that they were all civilians.
Foreign troops including US soldiers are stationed at Camp Chapman alongside Afghan soldiers.
A statement from the NATO mission in Afghanistan said it was "aware" of the blast, but did not elaborate.
In 2009, Camp Chapman was the target of a spectacular suicide attack claimed by Al-Qaeda. Seven CIA American officials were killed in the deadliest assault on the US agency since 1983, when eight officers died in an attack on a military base in Beirut.
Camp Chapman is located less than four kilometers (2.4 miles) from the city of Khost, which is near the Pakistani border, a volatile region where the Taliban but also a multitude of armed Islamist groups hold sway.
Earlier today, officials said at least two civilians had been killed in a roadside bomb blast, blaming the attack on the Taliban.
Four other Afghans and two police were wounded when a police vehicle hit the roadside bomb in Kunduz city today, provincial police spokesman Sayed Sarwar Husseini told AFP.
Roadside bombs have been the Taliban's weapon of choice in their war against foreign and Afghan security forces, now in its 14th year.
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