The coalition said it would reopen Hodeida port to receive "urgent humanitarian and relief materials" and Sanaa airport to UN aircraft from midday tomorrow (0900 GMT).
It did not specify when or if it would ease a blockade on commercial traffic.
Hodeida, which is controlled by Huthi rebels backed by Saudi Arabia's arch-rival Iran, is a key conduit for much- needed food and medicine imports to Yemen.
The missile was intercepted near Riyadh's King Khalid International Airport, sparking a war of words between Tehran and Riyadh, which accused Iran of "direct aggression" and supplying arms to the Huthis.
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The United Nations said Wednesday it had been notified by the Saudi authorities of the reopening on Thursday of the Yemeni ports of Hodeida and Saleef, as well as Sanaa airport.
"We are monitoring these developments and we are trying to see whether that actually takes place on the ground," UN spokesman Farhan Haq told reporters at UN headquarters in New York.
The UN Security Council on November 9 called for the blockade to be lifted, warning that otherwise Yemen would face "the largest famine the world has seen for decades".
The Huthi government yesterday announced the country's main international airport was fully functional again a week after a Saudi-led air strike destroyed the facility's navigation system.
The airport had been open to only select humanitarian flights.
Allied with Yemeni strongman Ali Abdullah Saleh, the Iran-backed Huthi rebels control the capital Sanaa along with much of northern Yemen.
More than 8,750 people have since been killed.
The country also faces a deadly cholera epidemic and millions stand at the brink of official famine.
The UN Food and Agriculture Organization (FAO) says Yemen is highly dependent on imported wheat for its basic needs.