They said the vessel was then taken to a port in Yemen.
Israel said the ship was not Israeli, and no Israelis were among its crew. Israeli PM Benjamin Netanyahu said this was "another act of Iranian terrorism".
Iran has not commented. Houthis had threatened to hijack Israeli ship within their reach over Israel's war with Hamas in the Gaza Strip.
Israel says 1,200 people were killed and more than 240 taken hostage during the surprise Hamas attack on the south of the country on 7 October.
Israel has launched a massive military operation - involving air and artillery strikes as well as ground troops - with the aim of eliminating Hamas.
The Hamas-run health ministry says the death toll in Gaza since then has reached 12,300. More than 2,000 more are feared to be buried under rubble.
The Houthis have fired several missiles and drones towards Israel just after Israel launched its retaliatory operation.
The US said at the time that all the missiles and drones were intercepted by its warship in the Red Sea.
The Israel Defense Forces (IDF) described the attack on the ship - which it did not name - as a "very grave incident of global consequence".
The IDF said the vessel was on its way from Turkey to India when it was seized in the southern Red Sea near Yemen.
Although Israel says the seized vessel does not have any connection with it, unconfirmed reports suggest the ship may have an Israeli owner.
In Sunday's statement on social media, Mr Netanyahu said that Israel "strongly condemns the Iranian attack against an international vessel".
He said the ship was owned by "a British company and is operated by a Japanese firm", adding that "25 crew members of various nationalities including Ukrainian, Bulgarian, Filipino and Mexican" were on board the ship.
Iranian Foreign Minister Hossein Amir-Abdollahian has recently said that what he called resistance groups allied to Tehran were "cleverly adjusting pressure" on Israel and its supporters.
Earlier this month, the Houthis shot down a US military drone off Yemen's coast, American officials said.
The Houthis have been locked ina prolonged civil warwith Yemen's official government - backed by Saudi Arabia - since 2014.
Yemen's Iranian-backed Houthi rebels say they have seized an Israeli cargo ship in the Red Sea.