The men belonged to the banned Jamaatul Mujahideen Bangladesh, which seeks to establish Islamic rule in the country.
A BBC report said the six executed included JMB head Abdur Rahman and his deputy Siddiqul Islam, known as Bangla Bhai. The executions took place at different jails across the country.
The Press Trust of India news agency reported a seventh person who was also convicted remains at large.
PTI said Bangladeshi President Iajuddin Ahmed had recently turned down the mercy petitions of the executed man.
Authorities tightened security throughout the country as a precautionary measure against any retaliatory action by the militants, the report said.