Police fired on the militants from banned group Jamayetul Mujahideen Bangladesh (JMB) whom officers had stopped by chance yesterday near the teacher's home in north Dhaka, a local police chief said.
Police arrested one militant and seized two syringes full of a poisonous liquid and a pistol, while two other suspected militants fled, Atiqur Rahman told AFP.
"Our patrol team stopped the car for routine check, but the three men got out and opened fire at us. Officers were forced to retaliate by firing live rounds," Rahman said.
The group believed that the teacher held anti-Islamic views, had forced a colleague to shave off his beard and had converted a prayer space into a classroom, another officer said.
More From This Section
The JMB was blamed for a series of blasts in 2005 including a synchronised attack across the Muslim-majority nation when more than 400 small bombs were set off killing at least two people.
The JMB was also involved in a spate of bombings on judges and courts deemed un-Islamic that left at least 28 people dead in 2005.
The group has been relatively quiet since an elite security force launched a nationwide crackdown on the group in 2006.
More than 1,000 JMB members were prosecuted and in 2007 an army-backed government hanged six of its top leaders including its founder and supreme head Shaikh Abdur Rahman.
In recent months, police have arrested several high-profile members in what security officials say could be a sign that the outfit may have regrouped with financing from overseas.
In February, attackers ambushed a prison van in the north and snatched three convicted JMB militants after killing a police officer.