"Our air defences were able to down an American MQ-9 while it was carrying out hostile surveillance and espionage activities in Yemeni territorial waters as part of American military support for Israel," the group said in a statement.
The US military did not immediately react to the statement.
The Iran-backed group, who are part of the "axis of resistance" of groups opposed to Israel, claimed responsibility for multiple drone and missile attacks against Israel during its war on Gaza.
"Hostile activities will not deter the armed forces of Yemen from pursuing their military operations against the Israeli entity and its oppression of the Palestinian people," the group added.
Houthis, opposed to government forces in Yemen, took control of Yemen's capital Sanaa in 2014.
Last week, Houthi rebels pledged more attacks against Israel if its war on Gaza continues, saying it had already fired drones and ballistic missiles in three separate operations.
"We will continue to carry out qualitative strikes with missiles and drones until the Israeli aggression stops," said a Houthi military statement aired on the rebels' Al-Masirah TV.
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