The explosion rocked the embassy around 10.45am, destroying the entrance of the complex, setting several cars ablaze and toppling trees.
The scene looked like "a war zone", one witness said.
Shocked US Marine embassy guards rushed to help evacuate the building and then, pistols in hand, cordoned off the area. A Tanzanian security officer at the embassy, Daniel Edson, said everyone was taken by surprise. "There was nothing unusual before the explosion," he said.
"I was in the visa section," said Amio Zara from her hospital bed, where she was being treated for head, hand and leg injuries suffered in the blast.
"I heard a loud bang outside and immediately felt pain in my head. I tried to run downstairs but the stairs had collapsed. I managed to get outside, I saw smoke and fallen trees before I collapsed," she added.
Fifteen of the wounded were kept in hospital for treatment.
The French and German embassies, both nearby, were damaged by the explosion but no one in either building was hurt.
Tanzanian President Benjamin Mkapa condemned the attack.
"Horrible and despicable," he said to reporters on arrival at the town of Victoria Falls in Zimbabwe, where he is due to join six other African leaders for a summit on the Congo crisis.
"We are going to try to unearth who is behind this ... When we do, we are going to take very stern measures indeed," he said.
"Attacks like this have never happened here before," said Richard Mngazija, deputy editor of Tanzania's Daily Mail. "Nairobi, yes, Mogadishu, yes, Cairo, yes, but Dar? Never.
"So when the explosion went off we thought it was an earthquake. Our office is maybe eight kilometres from the embassy. We could hear and feel the blast from here, it was that loud and powerful. But no one here thought of bombs or terrorism. We just don't have terrorists here."
So unprepared is Tanzania for this sort of event that the city fire brigade could not send any of its vehicles to the scene. Instead, one fire engine from the port, two from the airport and another from the army were summoned.Reuse content