Mohammed al-Moghrabi, 41, was sentenced to death for the June 25 rape and murder by a court run by the Shia Huthi rebels who control Sanaa.
The gruesome crime coincided with the first day of Eid al-Fitr, the Muslim holiday that marks the end of the holy month of Ramadan, and sparked anger among the population.
Moghrabi was first given 100 lashes and then made to lie flat, his face on the ground, and killed by multiple gunshots by security forces to cheers from the crowd.
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Police said they escorted him to Tahrir square where he was executed amid fears the angry crowd could lynch him.
The public execution was widely aired on Huthi-run media in Yemen, framed as an example of the Shia rebels' efforts to combat crime in their areas.
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The Iran-backed Huthis have been locked in war with the Saudi-backed internationally-recognised government of President Abedrabbo Mansour Hadi for two years.
More than 8,000 people have been killed and millions displaced in the conflict, while nearly 2,000 have died of cholera since April.
The United Nations has described Yemen as "the largest humanitarian crisis in the world," with 10 million civilians in acute need of life-saving aid as the country teeters on the edge of famine.
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