The attacker blew himself up inside US property, Ankara Governor Alaaddin Yuksel said. The blast sent masonry spewing out of the wall and could be heard a mile away.
Interior Minister Muammer Guler said the bomber was a member of a far-left group. The US State Department said it was working with Turkish police to investigate what it described as a terrorist blast.
Islamist radicals, far-left groups, far-right groups and Kurdish separatist militants have all carried out attacks in Turkey in the past. There was no claim of responsibility.
"The suicide bomber was ripped apart and one or two citizens from the special security team passed away," said Turkish Prime Minister Tayyip Erdogan, who was at a ceremony in Istanbul when the blast happened.
"This event shows that we need to fight together everywhere in the world against these terrorist elements," he said.
Far-left groups in Turkey oppose what they see as US influence over Turkish foreign policy.
However, the White House said it was not yet clear who was responsible for the bombing. A spokesman added: "The attack itself was clearly an act of terror."
Turkey is a key US ally in the Middle East with common interests ranging from energy security to counter-terrorism, and has been one of the leading advocates of foreign intervention to end the conflict in neighbouring Syria.
Around 400 US soldiers have arrived in Turkey over the past few weeks to operate Patriot anti-missile batteries meant to defend against any spillover of Syria's civil war, part of a Nato deployment due to be fully operational in the coming days.
US Ambassador Francis Ricciardone emerged through the main gate of the embassy after the explosion to address reporters, flanked by a security detail.
"We are very sad of course that we lost one of our Turkish guards at the gate," Mr Ricciardone said.
"It was a huge explosion. I was sitting in my shop when it happened. I saw what looked like a body part on the ground," said travel agent Kamiyar Barnos, whose shop window was shattered around 100 yards away.
State broadcaster TRT said the attacker was thought to be from The Revolutionary People's Liberation Party-Front (DHKP-C), which wants a socialist state and is anti-American, according to the US National Counterterrorism Centre.
The group, deemed a terrorist organisation by the US and Turkey, was blamed for a suicide attack in 2001 that killed two police officers and a tourist in Istanbul.
Mr Guler said the bomber could have been from the DHKP-C or a similar group. The DHKP-C has in the past attacked Turkish official targets with bombs.
The DHKP-C's most recent attack, on an Istanbul police station, was September 11, 2012, seen as a symbolic strike to coincide with the 11th anniversary of the al Qaeda attacks on the US.
Despite some strains, Washington and Ankara have long had a strong strategic alliance.
Turkish bases have helped US forces in Afghanistan, while Turkey hosts a Nato radar system, operated by US forces, to help defend against threat from Iran.
The US consulate in Istanbul warned its citizens to be vigilant, while the British mission called on businesses to tighten security.