Mark Lowcock, the UN under-secretary general for humanitarian affairs, urged the Saudi-led coalition to lift its blockade of the conflict-torn country.
On Monday, the coalition shut air, land and sea routes into Yemen after Houthi rebels fired a missile at Riyadh.
Saudi Arabia said the blockade was needed to stop Iran sending weapons to the rebels.
Iran denies arming the rebels, who have fought the Saudi-led coalition since 2015.
Mr Lowcock was speaking on Wednesday, after briefing the UN Security Council on the issue behind closed doors.
“I have told the council that unless those measures are lifted… there will be a famine in Yemen”, Mr Lowcock told reporters.
“It will be the largest famine the world has seen for many decades with millions of victims.”