It said it supported the UAE and any response to hijacking, which took place near the Red Sea port city of Hodeidah on Sunday.
Brig Gen Turki Al Malki, spokesman for the Saudi-led coalition fighting the Iran-backed rebels, confirmed on Monday that the cargo ship, the Rawabi, had been hijacked.
He said the Rawabi had been taking a Saudi field hospital from Yemen's Socotra Island in the Indian Ocean to Jazan in the south of the kingdom.
"The militia must promptly release the ship," Brig Gen Al Malki said, "or the coalition forces will undertake all necessary measures and procedures to handle this violation, including the use of force if necessary."
Separately, the US also condemned the hijacking.
"We urge the Houthis to immediately release the ship and crew unharmed and to cease all violence that sets back the political process to end the war in Yemen," State Department spokesman Ned Price said on Tuesday.
The GCC's Monday evening statement came after Kuwait condemned the hijacking. The country's Ministry of Foreign Affairs said it considered the incident a “criminal act that threatens global trade”.
It is not the first time the Houthi rebels have targeted shipping.
In November 2019, the Houthis seized two South Korean vessels and a Saudi-flagged tug in the Red Sea a few kilometres off Uqban Island, north of Hodeidah. In July the year before, Riyadh said the rebels attacked two Saudi-operated oil tankers in the Red Sea.
Also on Tuesday, the coalition said Saudi defences intercepted and destroyed five drones launched at the kingdom from Sanaa, the Yemeni capital.
It said “operational options” were on the table to respond to Houthi threats.
Drones and rockets are launched at Saudi Arabia on a near-daily basis, some landing in residential areas and causing civilian casualties.
The hijacking and rockets come as the Houthis push a ferocious assault on Marib, the Yemeni government's last northern stronghold. In November, the rebels took control of a large area south of Hodeidah.
Since the surge in fighting, the rebels have increased their rocket and drone attacks on Saudi Arabia and the coalition has stepped up its air strikes.
Saudi Arabia leads the Arab coalition that intervened in Yemen at the request of the internationally recognised government nearly seven years ago following the rebel takeover of the capital.
The civil war has caused what the UN has describes as the world's worst humanitarian crisis.
International attempts to stop the war have so far made little progress.
In late November, the UN said the war will have killed 377,000 people by the year's end, both directly and indirectly through hunger and disease.