Rohingya people have long been subjected to discrimination in Buddhist-dominated Myanmar, which denies them citizenship.
There were more than 300,000 Rohinya in refugee camps and makeshift settlements in Bangladesh even before the latest unrest.
Some 379,000 Rohingya Muslims have fled Myanmar's troubled Rakhine state for Bangladesh since new violence erupted last month, the United Nations said Wednesday.
The figure has risen by 9,000 in 24 hours, according to UN refugee agency spokesman Joseph Tripura told AFP.
Bangladesh authorities are now registering new arrivals and building a massive new camp near the border with Myanmar to accommodate the influx.
"We've already started shifting thousands of people to this camp where we're building sheds for them," Ali Hossain, government administrator for Cox's Bazar district, told AFP.