The UN said it would study whether the blockade amounted to "collective punishment," banned under international law.
The United Nations and Red Cross on Tuesday urged the Saudi-led coalition to reopen Yemen borders and allow imported food and medicine into the country.
"We call for all air and sea ports to remain open to ensure food, fuel and medicines can enter the country," Jens Laerke of the UN Office for the Coordination for Humanitarian Affairs said in Geneva.
An estimated 7 million people are facing famine in Yemen.
TRT World's Caitlin McGee reports.
The Saudi-led coalition fighting the Houthi movement in Yemen said on Monday it would close all air, land and sea ports to the Arabian Peninsula country to stem the flow of arms.
The Saudis and their allies say the Houthis get weapons from their regional rival, Iran. Iran denies the charges and blames the conflict in Yemen on Riyadh.
The UN Security Council is due to meet on Wednesday, at the request of Sweden, to discuss the humanitarian situation in Yemen, diplomats said in New York.
He said humanitarian operations are currently "blocked" because air and sea ports in Yemen are closed,
The Saudi-led coalition has told the world body to "inform all commercial vessels at Hodeidah and Saleef ports to leave," Laerke said, referring to Red Sea ports controlled by the Houthis.
The price of fuel jumped 60 percent "overnight" in Yemen and the price of cooking gas doubled, he said. "This is an access problem of colossal dimensions right now."
The International Committee of the Red Cross (ICRC) joined the call.
"Food, medicine and other essential supplies are critical for the survival of 27 million Yemenis already weakened by a conflict now in its third year," Robert Mardini, ICRC regional director for the Near and Middle East, said in a statement.
The ICRC said a shipment of chlorine tablets to prevent cholera did not get clearance at Yemen's northern border. It voiced fears about 50,000 vials of insulin for diabetics due to be delivered by next week, which require constant refrigeration.
ICRC spokeswoman Iolanda Jaquemet said a ship carrying 500 metric tonnes of rice, which arrived in Hodeidah port in October after a three-month trip from Pakistan, had to leave the port last week without offloading because the ship's crane had broken.
The port itself lacks adequate cranes after repeated coalition bombing.
Rupert Colville, UN human rights spokesman, said it would study whether the blockade amounted to "collective punishment", banned under international law but hoped that it would be temporary.
Attacks in Yemen over the past week have killed dozens of civilians, including children, at markets and homes, he said.
These included at least nine air strikes on the Houthi-held city of Sanaa since Saturday, when a missile was fired from Yemen towards the Saudi capital of Riyadh, he said.
A cholera epidemic has caused 908,702 suspected cases and 2,194 deaths since the outbreak began in April, WHO spokeswoman Fadela Chaib said.
In Berlin, German Foreign Minister Sigmar Gabriel called for increased aid to Yemen, citing alarm at the latest UN report. "No one will be able to say later, particularly with respect to Yemen, that they didn’t know what was happening.”