Ambassador Hassan Sayed Nam was not in the house when the attack took place in the diplomatic district of Hada, according to a security official.
One guard was killed, according to officials who said two of the 17 wounded were guards and the rest passers-by.
The blast left a hole in the outer wall of the house. Nearby homes and cars were also damaged.
The identity of the attackers was unclear.
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Violence has increased in Yemen since members of the Shiite Huthi militia, also known as Ansarullah, overran Sanaa in September.
The Huthis are accused of receiving backing from Shiite-dominated Iran.
Their attempt to advance in regions south of Sanaa has been met by deadly resistance from Al-Qaeda insurgents who are active in the country, as well as tribes in central Yemen.
It was not immediately clear if Wednesday's attack was carried out by a suicide bomber or if the device was remotely detonated.
Iran's Deputy Foreign Minister Hossein Amir-Abdollahian told the Arabic-language Al-Alam television channel that "no Iranian diplomat was wounded in the attack but the building was damaged."