The Houthi movement and its ally former president Ali Abdullah Saleh control much of northern Yemen, including Sanaa, and are battling a Saudi-led coalition that is trying to restore the internationally recognised government of President Abd-Rabbu Mansour Hadi.
The United States backs the Saudi-led coalition by providing it with intelligence and weapons.
"A military source said (Houthi) air defences shot down a U.S. MQ-9 surveillance drone in Jader area in the Sanaa province," SABA reported.
A Reuters photographer said the drone came down at around 11 am local time in a crowded area on the outskirts of the capital, but there were no reports of any casualties.
The charred wreckage of the aircraft was carried out by the Houthis aboard a Toyota pickup truck.
The Bahrain-based U.S. Fifth Fleet did not immediately respond to a request for comment.
More than 10,000 people have been killed in Yemens civil war. It began in March 2015 when the Houthis advanced on Hadisinterim headquarters in the southern port city of Aden, forcing him to flee the country and seek Saudi help.
The war has caused a humanitarian disaster in the country, where more than two million people have been displaced while around 750,000 are suspected to have been infected with cholera.