In a statement, Bangladeshi police said Rohingyas would not be allowed to travel anywhere outside of their allocated homes, not even to live with family or friends.
Transport operators and drivers have also been urged not to carry refugees, with landlords told not to rent out any property to them.
Analysts say the government wants to stop the Rohingya from disappearing into the general population and to keep them visible, in the hope of returning them to Myanmar - or even a third country.
What do we know about the new shelters?
According to Bangladesh's Daily Star newspaper, the new shelters will be on a site covering about 8 sq km (3 sq miles) of land, close to established camps which have been overwhelmed by arrivals from Myanmar.
A total of 8,500 temporary toilets will be built and 14 "makeshift warehouses" will be set up near the shelters, the paper says.
The new shelters are meant to be built within 10 days.
An ambitious plan, but is it plausible?
Jonathan Head, BBC Southeast Asia correspondent
Bangladesh faces a colossal task accommodating the now more than 400,000 Rohingyas who have fled Myanmar. It rightly demands a lot more international support. And that support has been slow in coming.
One reason is the dramatic surge in the numbers of new arrivals in a very short period of time. Another is the politics of aid in southern Bangladesh.
The UN refugee agency is not allowed to deal with the large numbers of Rohingya who are living outside of official refugee camps as they do not want these people to have refugee status. This is why the International Organization for Migration has been given a lead role. It is an agency with expertise in assisting and monitoring migrants but not in running large humanitarian relief efforts.
In this context, the plan to build 14,000 homes, and 8,000 latrines is ambitious. The ten-day timescale set by the government seems unrealistic. In reality, many tens of thousands of Rohingyas are surviving with no shelter and little food, with more arriving every day. No-one has yet drawn up a plausible plan for assisting them all.
How is the crisis affecting Myanmar-Bangladesh relations?
Tensions have been mounting, with Bangladesh's Prime Minister Sheikh Hasina heading to the UN General Assembly on Saturday to ask for more pressure to be put on Myanmar to help deal with the crisis.
The UN Security Council has appealed to Myanmar to stop the violence but no sanctions have been imposed.
Bangladesh has also lodged a formal protest with Myanmar about its use of military drones and helicopters which, it alleges, have violated Bangladeshi airspace on three days in the past week.
Bangladesh described their use as "provocative". Myanmar denies the allegation.
The two countries have also locked horns over the issue of landmines, with Myanmar denying Bangladesh accusations that its army is planting them on the border to prevent refugees from returning.