The move follows a week after the country's police issued restrictions on the movement of refugees.
Since late August, about 430,000 Rohingyas, mostly Muslims, fled to Cox's Bazar amid a military crackdown in Rakhine, which the UN dubbed as 'textbook ethnic cleansing.'
Law-enforcers have been on the alert to stop them from spreading out and now the telecom authority has come up with restrictions.
"According to inputs from the ground, the refugees are using mobile phones with SIMs of Bangladesh operators. SIMs are not supposed to be activated without subscriber registrations," State Minister for Telecom Tarana Halim said on Saturday.
"Some people are, however, selling their registered SIMs to the Rohingya refugees, which is a criminal offence," she told the media in Dhaka after a meeting on the issue.
Halim said they will start the process to identify SIMs used by the refugees.
"We will collect data of SIMs which have been activated since Jul 1 .The list of retailers in the area is also available. The number (of SIMs with refugees) will be clear after analysing those data."
Mobile phone users in Bangladesh have to go through a registration process, which requires providing fingerprints and a verification against the national ID database.
Bangladesh was already home to 400,000 Rohingya refugees before the latest influx, which began on Aug 25 when insurgents in Rakhine attacked 30 police posts.
Officials claim many of these Rohingyas are involved in criminal and terrorist activities.
By a government estimate, the latest wave of refugees saw nearly 430,000 Rohingyas pouring into the country.
Bangladesh has started collecting biometric details of newly-arrived and existing Rohingyas.
They are being provided with ID cards, which officials say can be used to access all kinds of support provided to the refugees.