Sudhir Suri, 58, head of the fundamentalist religious group called Hindu Shiv Sena, was shot in Amritsar, the local police said.
In the past, Suri had been accused of making derogatory and blasphemous comments against Sikhism and the Sikh community.
A senior police officer Arun Pal Singh told news agencies that “the assailant arrived on the spot and shot him dead in full public view”, adding that the radical leader had been shot several times.
Police later said that a local shopkeeper, Sandeep Singh, was arrested in connection with the shooting.
Punjab director general of police, Gaurav Yadav, was quoted as saying by the BBC that “whosoever is behind it and whosoever hatched the conspiracy will be unveiled and those who are behind it will be arrested”.
Local reports said that Suri was protesting outside a temple premises against its management, to protest the alleged desecration of Hindu deities, when at least five shots were fired by the assailant.
Just an hour before the attack on him, Suri had got into an argument with the management of the temple Gopal Mandir near Majitha Road over the alleged sacrilege of idols. He was also live on his Facebook where he showed his followers some Hindu idols “shamelessly dumped in the garbage”.
In the live, he said: “We will not tolerate such sacrilege, even if by fellow Hindus.”
The gunman was held on the spot and was found to be carrying a licensed weapon.
Suri was rushed to the hospital but he succumbed to his injury, according to reports.
NDTV, quoting unidentified sources, said that the attacker is a resident of the Sultanwind area in Amritsar and had arrived at the scene of the protest where Suri was in an SUV with three others. While the assailant was arrested, the other three escaped from the scene.
Police have launched an investigation.
Meanwhile, the authorities have also requested the local populace to maintain calm and not give in to any communal calls.