The Huthis fired at Tel Aviv a "new drone called 'Yafa', which is capable of bypassing the enemy's interception systems," the movement's spokesman, Yahya Saree, said on social media.
It struck "one of the important targets in the occupied Jaffa region, what is now called Israeli Tel Aviv," a Huthi statement said, adding "the operation has achieved its goals successfully".
Israeli authorities said an explosion hit an apartment building in Tel Aviv at 3:12 am (0012 GMT), killing one person and wounding four others.
The Israeli army said the blast was "caused by the falling of an aerial target", based on an initial inquiry. An Israeli military official who spoke on condition of anonymity said a "very big" drone had been detected but the alarm was not immediately raised because of "human error".
The Huthis pledged to turn Tel Aviv into a "primary target" after months of drone and missile attacks targeting shipping in the Red Sea and the Gulf of Aden in response to the Gaza war.
Hezam Al Asad, a member of the Yemeni rebel movement's politburo, called the strike "unprecedented".
In an interview with the pro-Iranian channel Al Mayadeen, he said the attack marked a "new phase" of operations against Israel which would increase in the coming period.
The Huthis have previously claimed attacks targeting the southern Israeli resort of Eilat and port cities of Ashdod and Haifa, but Friday's strike is the first operation claimed by the rebels against Tel Aviv.
The Huthis' military spokesman on Friday said the rebels "will focus on targeting" areas deep inside Israeli territory.
Saree declared the Israeli commercial hub "an unsafe area," saying it "will be a primary target within the range of our weapons".
Saree said the Huthis "have a bank of targets" in Israel, including "sensitive military and security targets".
They "will continue... to strike those targets in response to the enemy's massacres and daily crimes against our people in the Gaza Strip," he said.
On Saturday, Saree said the Huthis "will not hesitate to expand its military operations... until the aggression stops".
The threat came after the health ministry in Hamas-run Gaza said at least 90 people were killed and 300 wounded in a strike on Al-Mawasi camp for displaced people. Israel said the strike targeted Hamas military commanders behind the October 7 attack that sparked the Gaza war between Hamas and Israel.
Separately on Friday, projectiles struck a container ship off the coast of Yemen without causing any casualties, an attack likely carried out by the Huthis, maritime security firm Ambrey said.
"A Singapore-flagged container ship was 'hit' by projectiles" 80 nautical miles (148 kilometres) southeast of the Yemeni port city of Aden, Ambrey said, adding no injuries were reported in the attack that is consistent with previous Huthi operations.
The United Kingdom Maritime Trade Operations, which is run by Britain's Royal Navy, said a "vessel has been hit by unknown projectiles" southeast of Aden.
"All crew reported safe. Authorities are investigating," UKMTO said.
The rebels have attacked at least 88 commercial vessels since their anti-shipping campaign started in November, according to a tally compiled by the Washington Institute for Near East Policy think tank.
Huthi attacks have prompted some shipping companies to detour around southern Africa to avoid the Red Sea, a vital route that normally carries about 12 percent of global trade, according to the International Chamber of Shipping.
Egypt's Suez Canal on Thursday reported a 23.4-percent drop in revenues attributed to disruptions in Red Sea shipping over the past year.