“Two were medically evacuated to the Bagram base, one was treated at Camp Phoenix.”
Johnson was referring to the main US base near Kabul and another base inside the city.
The Afghan interior ministry and police confirmed the attack was carried out by a suicide car bomber.
Four Afghan passers-by were wounded by the blast, General Alishah Paktiawal, Kabul’s criminal police investigation chief, said.
Attacks have increased in Kabul in the past year as Afghanistan has suffered its bloodiest period since US-led soldiers toppled the Taliban movement from power.
In the last bombing in the capital, on August 15, a mine hit a convoy of 4WD vehicles, killing three policemen from the German embassy.
In other news, Britain’s defence ministry on Saturday released the names of three soldiers killed after a “friendly fire” incident a day earlier while fighting Taliban fighters.
Privates Aaron McClure, Robert Foster and John Thrumble, from 1st Battalion The Royal Anglian Regiment, were killed after being hit by a bomb dropped by a US fighter jet called in to give the soldiers air support when they came under fire from the Taliban.
Two other soldiers were injured in the incident near Kajaki dam in Helmand province.
The US, British army and Nato-led International Security Assistance Force, under which the dead soldiers were serving, have all said they will investigate.
Meanwhile, talks are continuing between South Korean officials and the Taliban to secure the release of the remaining 19 nationals kidnapped by the Afghan group five weeks ago, according to a South Korean diplomat.
“We’re closely in contact with them (the Taliban),” an unnamed official at the South Korean embassy in the capital Kabul said on Saturday.
But the diplomat and a Taliban spokesman denied that a deal had been struck to release the hostages as early as Sunday.
“We’re in telephone contact with the Koreans; however, there’s nothing new and talks continue,” Yousuf Ahmadi, a Taliban spokesman, said.
Earlier on Saturday, the Afghan defence minister revealed that the Afghan military called off a plan to attempt to rescue the original group of 23 South Koreans shortly after they were captured by the Taliban.
“A hostage rescue operation is a very complicated operation,” Abdul Rahim Wardak, the Afghan defence minister, said.
“To make it successful, it needs very elaborate intelligence, inside information. But what happened was the international community asked us not take military action and that was the repeated request of the South Korean government.”
Two of the hostages have since been killed and talks to free the others were have stalled after the Taliban released two women as a “gesture of goodwill”.