The figure has risen by 9,000 in 24 hours, the 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.
Attacks by Rohingya militants on Myanmar security forces in Rakhine on August 25 sparked a harsh military crackdown on the minority Muslim community and the exodus started almost straight away.
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.
These are now completely overwhelmed and tens of thousands of new arrivals have no shelter.
Most walked for days to reach Bangladesh and aid workers say many are sick and in desperate need of food.