The gunfight took place in a village in Fazilka district, where the police took the man to recover a weapon.
Naveen Arora, the son of RSS leader Baldev Raj Arora, was shot dead by two motorcycle-borne assailants at about 7 pm on November 15 when he was walking home from his shop. The attackers reportedly fired at him from point-blank range.
He was taken to the hospital, where the doctors declared that he had been brought dead.
On November 17, pro-Khalistan group Sher-e-Punjab Brigade claimed responsibility for the murder, accusing the RSS of "assimilating Sikhs into Hinduism in Punjab". The police have not confirmed the authenticity of the claim.
The newspaper quoted Arora's family as saying that despite several arrests in the matter, the police have not revealed the suspects' motive behind the murder.
On Thursday, the Ferozepur Police said that the prime accused, identified as Badal, was taken to the Mamu Joya village by a police team when two of his accomplices, who were hiding at the spot, opened fire at them.
Deputy Inspector General (Ferozepur Range) Harmanbir Singh said that Head Constable Balaur Singh got injured when a bullet hit his arm.
"The police also fired in retaliation, in which Badal was injured," The Indian Express quoted Singh as saying. "Both Balaur Singh and Badal were admitted to Fazilka Civil Hospital, where Badal succumbed to his injuries."
It was unclear if Badal was hit by the shots fired by his accomplices or those fired by the police in retaliation.
The two shooters fled the area, The Indian Express quoted unidentified police officers as saying. The police are searching for them and have widened their investigation into the murder case.
The police had on November 20 arrested Gursimran Singh alias Jatin Kali, another main suspect in the murder case, in a separate gunfight in Arifke village. Earlier that day, the police also detained two persons, Harsh and Kanav, India Today reported.