The bomber also died in the blast at the International Security Assistance Force (Isaf) base near the eastern city of Khost, they said.
The dead were all reported to be civilian staff at the base and no Nato troops were among the casualties.
The staff had been waiting at a checkpoint to enter the base for work.
"This [attack] was carried out by the enemies of our country," Khost governor Arasala Jamal said.
No-one has yet said that they carried out the attack.
There have been numerous suicide bombings in Afghanistan since 2005.
According to one estimate, there were 139 suicide attacks in the country last year with the upsurge in the Taleban-led violence.
Bloodshed in Afghanistan last year returned to levels not seen since the fall of the Taleban in 2001, with the southern provinces of Helmand and Kandahar, and areas in the east of the country particularly hard-hit.
Some 4,000 people are believed to have died in 2006 in the insurgency - about a quarter of them civilians.Güncelleme Tarihi: 20 Eylül 2018, 18:16