Shubhdeep Singh Sidhu, popularly known as Sidhu Moose Wala, was shot by unidentified people while he was travelling in the state’s Mansa district on Sunday evening. He was 28.
Two others were injured in the attack.
Police said they were investigating the incident, and that they suspected the involvement of gangs in the crime.
State police chief VK Bhawra had said on Sunday that a Canada-based gangster had claimed responsibility for the attack.
On Monday, Punjab’s chief minister Bhagwant Mann ordered an inquiry – led by a high court judge – into the incident and asked Mr Bhawra to issue a clarification over his statements.
Moose Wala’s murder has sparked a political storm in the state as opposition leaders questioned why the Aam Aadmi Party (AAP) government, led by Mr Mann, had scaled back security cover for the singer.
Police said that Moose Wala’s security detail had been reduced to two commandos from four, and that these officers weren’t travelling with the singer when he was attacked.
Moose Wala was among over 400 people in Punjab whose security detail was withdrawn or scaled back recently by the government.
Mr Mann had said the step was partly taken because of a government exercise to crack down on so-called “VIP culture” which privileges politicians above ordinary citizens.
Police officials said it was also done to deploy more personnel for security ahead of the upcoming anniversary of the controversial Operation Blue Star – when the Indian army stormed the Sikhs’ most sacred shrine in 1984.
But the government’s move had become controversial after the names of the people on the list were leaked on social media, with some pointing out that it increased the threat to their lives.