Vehicles set ablaze at the blast site in Kabul sent smoke rising into the air as emergency medical teams worked to get the injured to hospital.
General Mohammad Zahir Azimi, a defence ministry spokesman, confirmed the attack was a suicide bombing.
"Its target could be both Afghan and foreigners because it is an important area," he said.
In addition to the embassy and military base, the area houses United Nations offices.
One man who was injured told Al Jazeera: "There was an oil tanker refuelling and in front of me a car exploded. I saw it with my own eyes ... I saw a lot of injured people."
A Taliban spokesman confirmed to Al Jazeera that the group had carried out the attack, calling it a suicide mission.
|A wounded US soldier is stretchered out after the attack [Reuters]
The spokesman said the bombing was a victory for the Taliban as it hit a road that runs between Germany's embassy in Afghanistan and Camp Eggers, a US military base that trains Afghan security forces.
"Our target was the German embassy and US base, because both have troops here in Afghanistan," he said.
"We want to use more of these tactics if this kind of suicide attack gives a good result."
Kabul was hit by a number of attacks last year, fuelling speculation that the Taliban, which was ousted from power during the US-led invasion of the country in 2001, may again be gaining ground in areas surrounding the capital.
Barack Obama, the US president-elect, has vowed to send up to 30,000 more troops to Afghanistan after he takes office, which would effectively double the number of US forces in the country.