Iran's ambassador to Yemen, Hossein Niknam, was not at home when the bomb exploded at the residence in the capital, Sanaa, killing a security guard and his son, security officials said.
The blast heavily damaged several nearby buildings and punched a hole into the residence. An Iranian flag later lay on the debris.
The Yemeni officials spoke on condition of anonymity because they were not authorised to brief journalists.
"The Sanaa explosion didn't harm any Iranian diplomats. Only material damage was inflicted," Tasnim quoted Abdollahian as saying.
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Niknam is new to the post and only presented his credentials to the Yemeni Foreign Ministry within the last week, according to Iranian state media.
Al-Qaida in the Arabian Peninsula, Yemen's local branch of the terror group, later issued a statement on Twitter claiming the attack on the ambassador's house, located next to the headquarters of Yemen's main intelligence agency. The group has carried out similar attacks in Sanaa.
Local al-Qaida militants have been battling Houthis in the central region where the Shiite group and its allies aim to expand their territory.
Washington views al-Qaida in the Arabian Peninsula as the most dangerous branch of the terror group as it has been linked to a number of foiled or botched attacks on the US homeland.
The US has conducted a campaign of drone strikes in the country targeting suspected militants and offers aid to the country's military. Civilian casualties in the strikes have angered many.