Witnesses told Reuters that as many as six people died when the device, planted on the vehicle, exploded and blew passengers' bodies into the street, but that higher toll could not be immediately confirmed.
Separately, Yemeni police said they foiled a plot to carry out a suicide bombing inside a US language institute in Sanaa. An institute spokesman denied the report, saying a small incident involving the arrest of a motorcyclist trying to travel on a closed road that had been blown out of proportion.
The impoverished country, situated next to the world's top oil exporter Saudi Arabia, is battling a number of armed groups, including al Qaeda fighters who Washington said this month could be planning attacks.
Yemen's security personnel have been targeted by Islamist militants although most of the attacks have taken place in the largely lawless south and east of the Arabian Peninsula state.
Regarding Sunday's bombing, the air force spokesman told Saba news agency: "This cowardly terrorist act resulted in the martyrdom of one person and injured a number of others, several of whom are in a serious condition. They have all been transferred to hospital.".
Saba named the dead man as Sergeant Mohammed al-Shaghdari.
There was no immediate claim of responsibility.
Later on Sunday, a Yemeni police spokesman and a counter-terrorism official said security forces had detained a suspected al Qaeda militant trying to infiltrate the Yemen-American Language Institute (YALI) on a motorcycle.
The police spokesman said the man was found to be carrying an explosives belt and was detained when he tried to enter the compound posing as a student seeking to register for English courses. Another official said the man had been referred to the counter-terrorism department for further questioning.
A YALI spokesman said the report was untrue.
He said that a Yemeni motorcyclist was detained when he tried to pass on a road closed to traffic for security reasons near the institute and refused to heed demands to turn back.
Yemen has been gripped by turmoil since pro-democracy demonstrations erupted in early 2011 against then-President Ali Abdullah Saleh, who stepped down last year.
Suspected al Qaeda militants killed four Yemeni soldiers during an Aug. 11 attack on forces guarding the country's only liquefied natural gas (LNG) export terminal in the southern province of Shabwa.
In May 2012 a suicide bomber in army uniform killed more than 90 soldiers rehearsing for a parade in the heart ofSanaa.
Earlier this month, Yemeni authorities said that had thwarted a plot by al Qaeda to seize two major oil and gas export terminals and a city in the east of the country.
The United States and other Western powers shut their diplomatic missions across the Middle East, Africa andAsia after Washington said it had information about unspecified terrorist threats. Most legations have since reopened.
Additional reporting by Khaled Abdullah; Writing by Mahmoud Habboush