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 of the three guards at the residence was killed," another security official said.
The blast severely damaged the residence, leaving a hole in the outer wall. Nearby houses and cars were also damaged.
It was not immediately clear if the attack was carried out by a suicide bomber or if the device was remotely detonated.
The identity of the attackers was unclear.
Al-Qaeda in the Arabian Peninsula has vowed earlier to target Ansarullah revolutionaries, who are also called Huthis.