Teresa Sancristoval, of medical charity MSF, said fuel shortages meant many people were having to travel by foot.
The UN's representative in Yemen says the indiscriminate bombing of populated areas is against international law.
Air strikes have killed at least 1,400, more than half civilians, the UN says.
Saudi Arabia says the offensive is to restore Yemen's exiled president to power, weeks after the Shia Houthi rebels - backed by forces loyal to Yemen's former president - took over the capital Sanaa.
The Saudis on Friday said they regarded all of Saada province as a "military zone" and told civilians to leave.
The UN's humanitarian coordinator for Yemen, Johannes Van Der Klauuw, said he was "deeply concerned" by the impact of the latest air strikes on northern Yemen.
"Many civilians are effectively trapped in Saada as they are unable to access transport because of the fuel shortage," he added.
Up to 130 strikes took place across the country on Saturday targeting rebel buildings, weapons stores and camps, a coalition spokesman said.
A spokesman for the Saudi-led coalition, Brig Gen Ahmad Assiri, said it was in response to Houthi rebels firing shells into Saudi Arabia earlier this week, killing 10 people.
Hundreds of families have already fled Saada province, security officials and Houthi rebels say.
Population 'living in fear'
Teresa Sancristoval, the emergency coordinator for Doctors without Borders (MSF) based at Saada's al-Gumhary Hospital, described intense bombing overnight, with reports of up to 140 strikes hitting the city in total.
"There is no electricity, no working telephones... many civilians are suffering the consequences," she said.
The coalition's order to evacuate was not heard by everyone, she warned. Leaflets were dropped in Old Saada - the rebels' stronghold in Saada province - on Friday.