Police said several people were injured in the blasts at the Azimuddin High School gate, a kilometre away from the ground, around 9am on Thursday.
An unidentified attacker was killed after police traded heavy gunfire with the miscreants.
A Hindu housewife, Jharna Rani Bhoumik, also died after being hit by a stray bullet that pierced her hut, officials said.
RAB said a suspect with bullet wounds had been detained from the spot and taken to the Mymensingh Medical College Hospital (MMCH).
Constable Jahurul Haque, 30, was declared dead after police admitted him to the Khishoreganj Zila Hospital, said Deputy Civil Surgeon Habibur Rahman. "There was a deep wound behind his neck caused by a sharp weapon."
“A helicopter took the remaining six to Dhaka,” said Mymensingh Assistant Superintendent of Police (ASP) Nur-e-Alam. Eight injured persons were still at Khishoreganj Zila Hospital including four policemen.
The blasts caused panic among the thousands of devotees, who were beginning to gather near the ground. But the prayers were not disrupted, said Kishoreganj ASP Obaidul Hasan.
“That was probably a crude bomb. The facts are still unclear,” he said.
Maj Saiful Sajjad of RAB-14 identified the suspected attacker detained from the spot as Shafiul Islam, 19, alias Abu Mokaddel.
The detainee said he took part in the attack on order from his ‘Ostad’ (chieftain), the RAB official said.
Shafiul also claimed five others were with him but he did not know them.
Kishoreganj Model Police Station OC Mir Mosharraf Hossain said two others were also detained.
The attack in Kishoreganj followed the deadliest terror attack in Bangladesh that killed 20 hostages, mostly foreigners, at an upscale restaurant in the heart of the capital’s diplomatic estate.
Two police officers, who tried to enter the cafe, were killed by grenades hurled by the militants.
In Kishoreganj, Many were crossing the school to get to the ground when the police check-post near its gate came under attack.
Some said they quickly left the spot after seeing people running along the path leading to the ground.
The attackers were said to have been carrying sharp weapons, reported the media, but their number remains unclear.
Witnesses said police fired at the miscreants before being joined by Border Guard Bangladesh (BGB) and Rapid Action Battalion (RAB) troopers.
The attack by Islamist gunmen on Gulshan's Holey Artisan Bakery and O' Kitchen on July 1, for which the IS claimed responsibility, prompted the authorities to bolster security at every prayer grounds.
Police normally erect watch towers and install security cameras to keep an eye on congregations, but the Gulshan attack forced greater surveillance.
Local authorities say over a thousand police, RAB and Armed Police Battalion (APBn) personnel were securing Sholakia and the surroundings.