There has been no sign of protests since the curfew was imposed on Wednesday evening in six cities including the capital, Dhaka.
However, Bangladesh security forces on Friday arrested two professors from Dhaka University, where the protests first erupted earlier this week, an official said.
Police arrested Harun ur Rashid, dean of the social science faculty, and Anwar Hossain, dean of bioscience and general secretary of the university's teachers' association, in morning raids, Yusuf Haider, the acting vice chancellor, said.
The curfew was imposed after trouble flared on the university's campus on Monday, when army personnel reportedly manhandled students during a football match.
Students then defied an existing ban on all protests - part of the state of emergency the government has kept in place for months - and staged a string of marches demanding the army withdraw from the campus.
The students, many brandishing sticks, clashed with police who retaliated with tear gas.
|"This is a right move, we now have enough time to buy food and other essentials we badly need"|
Habibur Rahman, a school teacher in Dhaka
Non-students joined the demonstrations, which quickly escalated into full-scale riots and spread across the country, despite a government decision to close the campus army post.
One man was killed and nearly 300 were injured as protestors demanded an immediate restoration of democracy and an end to emergency rule, before the curfew was declared on Wednesday.
The measure temporarily shut down mobile phone services, cleared streets of protesters and forced people to stay home.
Violence subsided on Thursday, as security forces patrolled the streets and the authorities warned they would take stern action against disorder.
All universities and colleges in the six cities, including the 40,000-student Dhaka University, have been closed indefinitely.
Dhaka residents welcomed the temporary reprieve from the curfew of Friday, saying it will allow them shop for groceries and other necessities.
Habibur Rahman, a school teacher in Dhaka, said: "This is a right move. We now have enough time to buy food and other essentials we badly need."