According to estimates issued by UN workers in Bangladesh's border region of Cox's Bazar, arrivals since the latest bloodshed started two weeks ago have already reached 146,000.
Numbers are difficult to establish with any certainty because of the turmoil as Rohingya escape brutal operations by Myanmar's military.
However, UN officials have raised their estimate of the total expected refugees from 120,000 to 300,000, said Dipayan Bhattacharyya, who is Bangladesh spokesman for the World Food Programme (WFP).
"They are coming in nutritionally deprived, they have been cut off from a normal flow of food for possibly more than a month," he told Reuters news agency. "They were definitely visibly hungry, traumatized."
The surge of refugees, many sick or wounded, has strained the resources of aid agencies and communities that are already helping hundreds of thousands displaced by previous waves of violence in Myanmar. Many have no shelter, and aid agencies are racing to provide clean water, sanitation and food.
Bhattacharyya said the refugees were now arriving by boat as well as crossing the land border at numerous points.
Another UN worker in the area cautioned the estimates were not "hard science" given the chaos and lack of access to the area on the Myanmar side, where the military is still conducting its "clearance operation".
The source added the 300,000 number was probably the worst-case scenario.
The latest violence began when insurgents attacked dozens of police posts and an army base. The ensuing clashes and a military counter-offensive killed at least 400 people and triggered the mass exodus of villagers to Bangladesh.
"She says she's seen levels of destruction that are unimaginable. All the villages have been destroyed," reported Al Jazeera's Florence Looi from Myanmar's capital Naypyidaw. "We are hearing reports that fighting is still going on."
UN spokesman Stephane Dujarric said on Wednesday from New York that WFP is appealing for $11.3m to support the influx of people and those already living in camps. Dujarric described women and children arriving there as "hungry and malnourished".
The crisis in restive Rakhine state is the biggest to face Myanmar's leader Aung San Suu Kyi, and her handling of it has been a source of disillusionment among the democracy champion's former supporters in the West.
In a statement on Wednesday, she blamed "terrorists" for "a huge iceberg of misinformation" on the strife in Rakhine. She made no mention of the Rohingya who have fled.
Myanmar's National Security Adviser Thaung Tun said the group that attacked 30 police posts two weeks ago is trying to carve out a separate Muslim state from the Buddhist-majority nation, and the armed forces are using maximum restraint in their operations against them.
Based on the prediction that 300,000 could arrive in Bangladesh, WFP calculated it would need $13.3m in additional funding to provide high-energy biscuits and basic rice rations for four months.
Bhattacharyya called for donors to meet the shortfall urgently.
"If they don't come forward now, we may see that these people would be fighting for food among themselves, the crime rate would go up, violence against women and on children would go up," he said.