Two other policemen sustained injuries when some 15 masked men jumped out off a bus and opened fire at a prison van that was taking the militants to a court in Mymensingh from Kashimpur Central Jail on the outskirts of Dhaka.
All the three freed militants were convicts and two were on death row while the third was serving a life term. They were convicted for their role in a series of bomb attacks across Bangladesh in 2005.
A massive manhunt has been launched to recapture death row convict Jahidul Islam alias Boma Mizan (38) and Salauddin Salehin alias Sunny who was serving a life term.
"We have recaptured Rakib Hassan from Sakhipur area of Tangail district," a police spokesman told reporters without giving details.
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Policeman Habibur Rahman, who was injured in the attack, told the media, "A bullet pierced through the windshield and hit me in the abdomen while (fellow policeman) Atiqul Islam died instantly as he was badly hit. They were firing and exploding bombs indiscriminately."
Police have announced a bounty of Taka 200,000 (USD1=Tk80) for each of the three escaped men.