Four American soldiers were killed in a separate incident.
The Ministry of Defence said the suicide bomber detonated the device near to the entrance to Camp Bastion, the main UK base in the country.
An MoD spokesman said the injuries were not life threatening.
At least two Afghan civilians were killed and several others injured in the blast.
It is believed the bomber walked up to a crowd of truck drivers before detonating his explosive vest, a spokesman for the International Security Assistance Force (ISAF) said.
The injured civilians and ISAF personnel were treated at medical facilities inside Camp Bastion.
An ISAF spokesman said: “The number of civilians killed and wounded is not confirmed as the investigation continues.”
In a separate incident four US service members were killed in a "complex attack" in the east of the country. The US military gave no further details about the incident.
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