The unrest first erupted Monday night at a soccer match at Dhaka University with students demanding an end to the six-month-long emergency rule.
As the unrest, which has claimed at least one life and injured 100 others, spread to others cities, the BBC reported authorities clamped an indefinite curfew in the capital and five others cites.
Higher educational institutions in those cities were closed and the students told to leave, the report said. Television stations are barred from airing footage of the violence.
Fakhruddin Ahmed, head of the caretaker government, was quoted as telling the nation late Wednesday the curfews would be temporary. He blamed "evil forces" and opportunists for the troubles.
The report said the protest appeared to be growing as people from various walks of life joined the students to demand the restoration of democracy.
The interim government came to power in January with a promise to eradicate corruption and to hold elections by the end of 2008. But people have grown restive mostly because of rising cost of living.