The clerics are accused of ordering 14-year-old Mosammet Hena to receive 100 lashes in a fatwa or religious edict at a village in southwestern Shariatpur district, the area's police chief AKM Shahidur Rahman said. The area is 35 miles (56 kilometers) from the capital, Dhaka.
Fatwas are illegal in Bangladesh, a Muslim-majority nation governed by secular laws.
But Islamic clerics are found presiding over courts that use Sharia law and issue fatwas to deal with issues like extramarital relationships. Such incidents usually occur in remote villages where police don't have quick access.
The girl collapsed after she was lashed in public with a bamboo cane about 70 times on Monday, Rahman said. She was taken to a hospital where she died hours later the same day, the officer said.
Rahman said the 40-year-old man with whom Hena was allegedly involved was also sentenced to 100 lashes. But the man fled, escaping the punishment, he said.
"We are hunting for the man," Rahman said.