The Taliban claimed responsibility for both attacks and said German military personnel in Kabul and other foreign troops in the east were the targets.
U.S. military spokesman Col. Jerry O'Hara said one U.S. service member died from wounds received in the 9:45 a.m. attack on a busy Kabul street. The blast also wounded six American forces and one U.S. civilian, he said.
"They detonated this explosive device right in a crowded area that was both used by civilians and military people," O'Hara said.
Firefighters and soldiers doused burning vehicles in the street near the base with water. Afghan security personnel and U.S. soldiers carried a U.S. service member out of a window near the blast.
Four Afghan civilians died in the blast and at least 19 wounded were being treated at two hospitals, the interior minister said. Two other wounded civilians were at other hospitals, said Gen. Mohammad Zahir Azimi, the Defense Ministry spokesman.
The German Embassy shares a small, two-lane road with Camp Eggers, a U.S. base that serves as the headquarters for soldiers training Afghan police and army personnel. Dozens of armed Afghan security personnel guard the street, and blast walls of concrete and sand-filled mesh-wire boxes line the road.
"It did not breach the wall (of the base)," said Lt. Col. Chris Kubik, a U.S. military spokesman. "It was fairly close but I can't tell you if they were targeting us or not."
A spokesman for the German Foreign Ministry in Berlin said "some personnel" were wounded in the blast, but he did not give numbers. He said they had no reports of deaths.
Windows inside the German compound shattered in the explosion, but the wall protecting the compound is still intact, he said. The spokesman refused to give his name for publication, citing government policy.
A Taliban spokesman, Zabiullah Mujahid, said a Taliban suicide bomber named Shumse Rehman carried out the attack in a Toyota Corolla. He said the bomber targeted two vehicles believed to be carrying German military officers.
"The Germans have forces in the north of Afghanistan and they are involved in the killing of innocent Afghans. The Taliban will target all those countries who have forces in Afghanistan," he said.
Mujahid said the Taliban had been monitoring the movements of German vehicles and planned the attack to target officers believed to be inside.
German Foreign Minister Frank-Walter Steinmeier condemned "this cowardly act of barbarity."