The withdrawal would begin on May 11 at 10 a.m. (0700 GMT), the head of the Houthis' Supreme Revolutionary Committee, Mohammed Ali al-Houthi, said on Twitter on Saturday.
The rebel pullback is a first step in implementing a hard-won ceasefire deal reached between Yemen's internationally recognised government and the Houthi rebels late previous year.
It calls for coalition forces to leave positions around the outskirts of Hodeidah in the initial redeployment, before a second phase in which both sides pull back further.
This development has come as an important part of a ceasefire agreement that has reached past year in December in Sweden, Al-Jazeera reported.
The information minister of Yemen's internationally recognized government, Moammer al-Iryani, warned of "attempts by the (Houthi) militia to mislead" the U.N. Security Council before an expected meeting in the coming week.
Yemen's warring parties started fresh United Nations -sponsored talks in Jordan on Monday, Yemeni officials said, two days after Houthi forces began withdrawing from the ports of Hodeidah, breaking a six month stalemate.
The Saudi-led coalition claimed the rebels are using the ports to smuggle weapons, while the rebels say they would be starved of vital supplies if the coalition held control over them.
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The Houthi-run al-Masirah TV channel said United Nations observers were monitoring the forces' withdrawal.
The UN statement comes a day after the Yemeni government accused the rebels of "staging a new ploy" by faking the withdrawal.
The Houthi withdrawal represents a " potential breakthrough", Adam Baron, a Yemen expert at the European Council on Foreign Relations think-tank told AFP. The statement said the airstrike also wounded 17 people, including 11 children.
The conflict in Yemen has already claimed tens of thousands of lives and put millions on the brink of starvation in what was already the poorest country on the Arabian Peninsula.
Britain's Foreign Secretary, Jeremy Hunt, tweeted there were "encouraging signs" in Hudaydah, with reports that Houthis were "beginning to withdraw (under United Nations supervision) from the Yemeni ports of Hodeidah, Saleff and Ras Issa". The coalition had disputed an earlier unilateral withdrawal by the Houthis from Hodeidah port in December, saying they had handed it over to coast guard members loyal to the group.
The port of Hodeida is one of Yemen's most important lifelines.
The military coalition intervened in March 2015 when President Abedrabbo Mansour Hadi fled into Saudi exile after the rebels took swathes of the country.