At least two men were shot dead in the vicinity of the restaurant, officials said.
Kabul police spokesman Hashmat Stanikzai said the attack took place just after dark against the Lebanese restaurant Taverna in the diplomatic quarter.
A single, loud explosion could be heard, followed by automatic weapon fire around the restaurant for about 20 minutes.
Deputy Interior Minister Ayoub Salangi said that the suicide bomber died in the attack and two other men were shot and killed in the vicinity of the restaurant.
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There are a number of embassies, foreign non-governmental organisation and Afghan officials living in the area. The restaurant itself was heavily fortified.
Salangi said police were engaged in a clearing operation around the restaurant late Friday night. No gunfire could be heard for at least 30 minutes after the initial burst of automatic weapon fire.
Taliban spokesman Zabihullah Mujahid claimed responsibility for the attack, which he said targeted foreign officials.