Bangladesh slapped a ban on more than one person riding pillion on a motorcycle today, a day after the wife of a prominent anti-terror police official was shot dead by three men riding a motorbike.

Mahmuda Aktar, the wife of Superintendent of Police Babul Aktar, known for battling Islamist militants, was stabbed and shot dead by the three in the southeastern port city of Chittagong.

"Only two people are allowed to ride a motorcycle, not three," Interior Minister Asaduzzaman Khan told reporters, adding motorcyclists will not even be allowed to carry a spouse and child, common across South Asia.

Bangladesh imposed a similar ban late last year after two foreigners were shot dead by three masked men riding on a motorcycle.

An elderly Christian grocer was also hacked to death on Sunday. Both attacks appeared to be the work of Islamist militants who have killed at least 30 people, including religious minorities, liberal bloggers and academics, since February last year, police said.

Islamic State and al Qaeda have claimed responsibility for many killings but the government denies either group has a presence in Bangladesh and says home-grown radicals are responsible.