According to UN figures, about 18,000 children between five and 17 die each year because they cannot swim.
The education ministry says rural ponds and lakes will be made suitable for lessons and university pools opened up.
But some say the directive will be hard to implement because of a lack of pools in urban areas.
Drowning has been described as a hidden epidemic in Bangladesh, one of the most densely populated countries in the world and situated in the low-lying Ganges River delta.
The victims are mostly children from poor sections of society who live close to major rivers, ponds and lakes.
Ponds are the main bathing place for more than two-thirds of the country's 160 million people.
Education Secretary Nazrul Islam Khan told AFP news agency that an average of 48 people drown every day in Bangladesh.
"It's a huge figure, which is 20 times higher than Australia," he said.
He said one in four deaths of children under four was caused by drowning.
The BBC understands the government is to ask schools to provide monthly progress reports.
Experts say the country has been successful in preventing child deaths caused by diarrhoea and other diseases but drownings have not attracted as much attention.
BBC Bangla's Sabir Mustafa says that children in rural Bangladesh grow up with water all around them and learn to swim from an early age, but children in urban areas, particularly the large cities, often have very little to do with water.
He says that the directive will be hard to implement because there are too few swimming pools in towns and cities.
He says there is an acute shortage of playgrounds in general, particularly in the biggest city Dhaka, and in many areas ponds and lakes have been filled up.
The government of Bangladesh has made swimming lessons compulsory in schools, to reduce the number of children who drown in the country's many waterways.