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.
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 today'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.
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