The Minister for Public Works, Naeem Akhtar, who was on a tour of Tral in south Kashmir, escaped unhurt in the attack.
"The grenade was reportedly hurled at 11.45 am," a police official said.
The explosion killed 17-year-old Pinky Kour and 56-year- old Ghulam Nabi Trag, the official said, adding 34 others, including 7 security personnel, were injured.
"I am unhurt myself but I am very sad because this claimed two lives...I feel very sad for them," Akhtar said.
A driver was "very critically injured", the minister said, adding that he was being airlifted to Srinagar.
"Innocent Kashmiri blood has been shed on one hand and on the other hand, they chose the eve of Islamic New Year to carry out this cowardly attack," Akhtar told PTI.
After the attack, Union Home Minister Rajnath Singh, Governor N N Vohra, Chief Minister Mehbooba Mufti, Deputy Chief Minister Nirmal Singh, other ministers and several legislators called up Akhtar to enquire about his well being, an official spokesman said.
In a statement, the chief minister said, "we shall have to ponder over as to how long this senseless bloodletting is going to consume us."
She added that "the vicious cycle of violence, which unfortunately has engulfed the state for three decades now, needs to be broken to stop the bloodshed and provide a breather to the people who have been choked by it."
She went on to question as to how long the people are going to "suffer like this on human, developmental, economic, educational and social fronts"
Leader of the opposition National Conference Omar Abdullah also condemned the attack on the minister.
"Condemn this militant attack. Glad Naeem Akhtar Sb is safe & well. My sympathies to families of the deceased & prayers for the injured," Omar tweeted.
Significantly, the attack took place on a day BJP general secretary Ram Madhav said here that the Jammu and Kashmir government and the Centre are open to having an unconditional dialogue with all stakeholders, including separatists, to address the problems of Kashmir.
Akhtar said the attack was an attempt to "subvert our outreach programme and our programme to take governance to the people".
He said the security forces exercised a "lot of restraint" while dealing with the aftermath of the explosion.
"I am profoundly shocked that they chose to target us when we were trying to speed up development of Tral constituency," Akhtar said.
"We have to introspect. The security forces respond to situations as lives of so many people are at stake in case of an attack. I do not think anyone died due to bullet injury. I think forces showed a lot of restraint," he added.
"Unfortunately, the incidents of violence like today's grenade attack are only aimed at reversing the developmental process which was initiated in Tral area.
"People of Tral like other places too want dependable basic amenities and other facilities and they have every right to demand it from the government and elected representatives," he said.
He urged the people of Tral to analyse themselves for how long such incidents can keep the area out of bounds for development.
"As of now, works worth Rs 100 crore are underway in Tral and our focus is to work in such a way so as to make up for the lost time," he added.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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