The 45-year-old, the district chief of Hindu Sangharsh Sena, was rushed to the city's Escorts Hospital but had died by the time he reached.
Mr Sharma was with a friend when the attackers opened fire at him.
"He was brought to the emergency wing of the hospital where a team of doctors declared him brought dead. There were around 15 injury marks on his body, including 8 bullet marks," the hospital's director, Dr HP Singh, said.
According to Amritsar police chief SS Srivastava, the CCTV cameras installed at various locations had captured the murder and they were scanning the footage for clues. The police are also trying to build a portrait of the suspects on the basis of the witness accounts, according to news agency Press Trust of India.
The police said one of the two men who opened fire was sporting a turban.
The police chief said some of his relatives and friends had suggested Vipan Sharma had feared for his life because he had spoken out against events to mark the anniversary of Operation Bluestar, an Indian Army action in 1984 to flush out terrorists from the Golden Temple. He was also reported to have sought police protection.
The incident comes two weeks after a local RSS leader Ravinder Gosain was killed in Ludhiana, Punjab's industrial hub. Mr Gosain was returning from an RSS drill when two men on a motorcycle shot him dead.
Shiromani Akali Dal chief Sukhbir Singh Badal condemned the killing and hit out at the ruling Congress government for its handling of the law and order situation in Punjab, saying that a "wave of violence had been sweeping through the state" with criminals not being brought to justice.
Chief Minister Amarinder Singh also came under attack from the Punjab Shiv Sena, who warned the government that it risked allowing the state to "plunge into the dark days of terrorism" if immediate corrective steps were not taken.
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