The vehicle was carrying Britons who were wounded in the explosion in Kandahar city, said Colonel Steve Bowes, a Canadian commander with the US-led coalition.
Two of the Britons were in serious condition, while the other two were lightly wounded, Kandahar governor Asadullah Khalid said.
He said the four were working on a customs project in the city.
At least two Afghan passers-by were hurt in the blast on a main road about a kilometre from a US military base, not far from the city centre, they said.
A spokesman for the British embassy said there had been an attack involving Britons in an armoured vehicle in Kandahar, but did not give any further details.
"We are aware of an incident involving a vehicle convoy involved in embassy business in Kandahar," spokesman Keith Scott said. He had no information about casualties.
Interior Ministry spokesman Yousuf Stanizai, however, confirmed the attack and said an investigation was under way.
US soldier killed
Earlier, a US soldier was killed by an explosion in the southern province of Helmand, the US military said in a statement late on Saturday night.
The incident took place near Geresk, the provincial capital of Helmand province on Friday evening, according to the statement.
"The unit was conducting an offensive patrol in the area of recent enemy activity when an explosive device detonated mortally wounding the soldier," the US military statement said.