The Indian employer of the man, who had claimed to be his father in order to get him the Aadhaar card, was also arrested, a police official said.
The Rohingya man, Mohammad Ajamuddin alias Molla Ajamuddin, and his employer Riyazuddin Molla, 36, a native of West Bengal, were arrested from the Burma huts in the Balapur area, he added.
Both the men were in the clothing business and had recently come to the city from Kolkata, the police said.
"Ajamuddin belongs to Myanmar and he and his family were living at Cox's Bazar in Bangladesh as refugees. About a year ago, Molla went to Bangladesh for some work related to his garment business and got acquainted to Ajamuddin," the official attached to the Rachakonda Police Commissionerate said.
"Molla informed Ajamuddin that he could earn more money in India and gave his phone number to him. Subsequently, Ajamuddin came to Kolkata and met him. Since then, he has been working for Molla for a monthly salary of Rs 6,000. Molla was providing shelter to him illegally," he added.
Molla also allegedly helped Ajamuddin get an Aadhaar card by giving false information to the UIDAI authorities, stating that the latter was his son, and violated the provisions of the Foreigners Act, the official said.
Acting on a tip-off, the police arrested the duo and seized their Aadhaar cards.
A case was registered against the two under IPC sections 420 (cheating), 468 (forgery for purpose of cheating), 471 (using as genuine a forged document) and relevant sections of the Foreigners Act, the official said.
Last month, the Rachakonda police had arrested a 20-year-old Rohingya man, who allegedly claimed to be an Indian citizen and applied for a passport to enable him to go to Dubai. The police had also seized a PAN card from him.
Scores of Rohingya Muslims from Myanmar's Rakhine state have been fleeing the restive region since August amid a fresh wave of violence, triggering a refugee crisis in neighbouring Bangladesh and India.
Union minister Kiren Rijiju had recently said the Rohingya Muslims were illegal immigrants and pitched for their deportation.