Bangladesh has cut services to millions of mobile phones along its border with India for "security" reasons amid fears a new citizenship law passed by its giant neighbour could prompt an influx of migrants.

The country's telecom regulator ordered the mobile shutdown late Monday along a one-kilometre (0.6-mile) band along the Indian frontier, the watchdog's spokesman Sohel Rana said.

The directive was issued "for the sake of the country's security in the current circumstances," the spokesman told AFP.

Bangladesh shares a 4,000-kilometre (2,500-mile) border with India and the shutdown would affect some 10 million mobile phone users, according to a top official from one operator.

"A large number of people in the border area will be without internet, voice and other mobile services," said S.M. Farhad, a spokesman for an industry association of local telecom operators. Officials from the Bangladesh Telecommunication Regulatory Commission said that the move was prompted by fears of fallout from India's new Citizenship Amendment Act, which accords rights to refugee migrants from neighbouring countries but excludes Muslims.

"We are worried that India's current condition may prompt many people to enter Bangladesh," said a BTRC official, speaking on the condition of anonymity.