Iran has condemned Sunday's abduction.
The official said armed men stopped the diplomat's car and forced him into their vehicle before speeding away. He did not disclose the diplomat's name or any further details, saying the incident was under investigation.
The official, speaking on condition of anonymity according to regulations, said traffic at the time of the kidnapping was light.
Yemen President Abed Rabbo Mansour Hadi has warned that the al-Qaeda branch in the country is using assassinations and abductions of foreigners as a way to challenge the central government's authority.
The United States considers the Yemen branch to be al-Qaeda's most active and dangerous.
In Tehran, a Yemeni diplomat was summoned to the Foreign Ministry to receive a formal protest, Iranian state TV reported. It said Iranian Foreign Minister Ali Akbar Salehi called his Yemeni counterpart.
Salehi condemned the kidnapping and called for serious action by the Yemeni government to free the Iranian diplomat, the TV report said, without identifying him.
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