Authorities say about 30 kilograms of explosives were packed into the car. The blast heavily damaged the embassy and destroyed its gate and nearby vehicles in the upscale residential district of the Pakistani capital. A huge crater was gouged into the road outside.
All of the dead are reportedly Pakistani, including two police officers.
Pakistani Foreign Secretary Salman Bashir visited the scene of the bombing and called it a "very devastating attack."
In Copenhagen, Danish Foreign Minister Per Stig Moeller called the bombing cowardly and "totally unacceptable."
Rehman Malik, the Interior Ministry's adviser to the Pakistani prime minister, told journalists that investigators are still trying to confirm exactly who carried out the attack. No one has claimed responsibility.
Malik says security officials believe the suicide attacker was targeting the Danish Embassy in reaction to an editorial cartoon that was republished by a Danish newspaper in February. He said the embassy had been receiving threats for a long time.
"This is a very sad incident, and it's a tragedy for the whole nation," Malik said.
Originally published by Danish newspapers in 2005, the controversial cartoon infuriated Muslims around the world by depicting the Prophet Muhammad wearing a turban with a bomb in it. Since Muslims consider any depiction of the Prophet Muhammad as blasphemous, a cartoon depicting him as a terrorist hit a particularly sensitive nerve in the Muslim world -- leading to violent protests in 2006 that included attacks on Danish diplomatic missions around the world.
The newspaper cartoons also have led to calls within Afghanistan for Denmark to withdraw its 700 soldiers from the NATO-led International Security Assistance Force.
The blast also raises concerns about a peace accord that was signed last month between pro-Taliban militants and the local government in the Northwest Frontier Province. Security analysts had warned that the truce would give militants space to plan and carry out new attacks in other parts of Pakistan, as well as in neighboring Afghanistan.
Pakistani officials said they are doing everything they can to protect all foreign diplomats and embassies.
RFE/RL's Radio Free Afghanistan contributed to this report, which also incorporates agency material