People who have returned from abroad since March 1 and staying at addresses different than the ones in their passports have been asked to contact nearby police stations.
All returnees must inform police about their current locations and provide mobile phone numbers, a notification from the Police Headquarters said on Tuesday.
It warned of legal action if anyone violates the directive, according to a news agency report.
Thousands of Bangladeshis returned home from countries affected by coronavirus in recent weeks but only a fraction of them have gone through home quarantine. The government has called out the Armed Forces to assist the civil administration to help tackle coronavirus or COVID-19.
Earlier in the day, rail and river transportations were shut down. Mass transportation will remain shut from March 26 to April 04.
Bangladesh, which has so far confirmed three coronavirus deaths and 33 cases, is taking sweeping measures to contain the virus. It has cancelled Independence Day programmes, closed educational institutions, and declared general holiday from March 26 to April 04.
The global death toll from coronavirus or COVID-19 reached 16,510 as of Tuesday -- a mortality rate of 14 per cent. The virus has so far infected 378,842 people since it was first reported in China, according to worldometers.
Of them, 260,268 are currently being treated and 12,062 are in serious or critical condition. So far, 102,064 (86 per cent) patients have recovered.