The missile was shot by Houthi militias targeting various Saudi areas, mainly border cities.
More than 10,000 Yemenis have been killed since the war began, tens of thousands have been wounded, and another two million people have been displaced.
The UN Security Council met behind closed doors on Monday at the request of the United Kingdom to be briefed on the situation after heavy clashes were reported in Yemen's third largest city on Friday and Saturday.
UN Secretary General Antonio Guterres said there are "intense negotiations" and his Yemen envoy is involved in shuttle diplomacy to stave off the attack. "I hope that it will be possible to avoid a battle for Hudeida", Guterres said.
Griffiths is set to present a new peace plan for Yemen on Monday, but he has warned that military action could derail that effort. "But if Hodeidah city is attacked it might be hard as we can't risk sending our staff to the frontline".
The spokesman of the Arab coalition Col Turki Al Malki stressed in a press conference on Monday the need to protect civilians and sustain the flow of aid.
His efforts to convince the rebels to hand over control of Al Hodeidah to UN-supervised global forces had failed, according to reports.
The United Nations pulled all of its global staff out of Hodeida early Monday morning.More news: Three Californias? Measure to split state heads to November ballot
Mr Griffiths held several rounds of talks last week in the Yemeni capital of Sanaa, which is held by the rebels.
U.S. Secretary of State Mike Pompeo on Monday called on all parties "to honour their commitments to work with the U.N".
The United Nations is racing to avoid an imminent offensive on a major Yemeni port city considered a lifeline for the country's war-ravaged population.
The UN Security Council is conducting an urgent meeting over the expected assault on Yemen's Hodeidah.
The conflict escalated in 2015 when Saudi Arabia and its Sunni-Arab allies - who accuse the Houthis of serving as Iranian proxies - launched a massive air campaign in Yemen aimed at rolling back Houthi gains.