Police and witnesses said unidentified assailants repeatedly shot the minister's brother, Muhammad Akram, in his hometown of Bijbehara, 45km south of the capital, Srinagar, on Thursday evening.
Bijbehara is also the electoral constituency of Kashmir's chief minister, Mufti Muhammad Sayid.
Akram, a contractor, was taken to hospital but was declared dead by doctors.
So far, none of the fighting groups active in the state have admitted responsibility for slaying the minister’s brother.
India faces a rebellion by Muslim separatists in the Himalayan state. Thousands of people have died in the 16-year-old insurgency.
Valley body count
At the time of the killing, both the chief minister and the interior minister were away in Jammu, the state's winter capital, about 300km south of Bijbehara.
The incident came hours after the interior minister had in a written reply told the state assembly, now in its budget session in Jammu, that as many 15,320 civilians and 4051 security personnel were killed and about 30,000 people, including 10,773 security personnel, were wounded in violence across the state over the past 14 years.
Thursday's killing took place in
the chief minister's hometown
He gave no figure for the number of separatist fighters killed during this period.
In other incidents, suspected separatists abducted two men, identified as Muhammad Amin Lone and Hilal Ahmad Lone, from their respective residences in a village in northwestern Baramulla district and executed them.
Police said another person, Mumtaz Ahmed Lone, was targeted at Bandipore, a town in the north of Kashmir valley.
Mumtaz was working for the counter-insurgency special operations group of the state police, officials confirmed.
Another resident, Gulzar Ahmed Wani, was kidnapped from his home at Wahipora in southern Pulwama district and later shot dead.
Kashmir has seen a steady fall in
the number of violent incidents
Also on Thursday, police found the corpse of a man in a remote village of neighbouring Anantnag district.
The body could not be identified immediately, officials said.
In a firefight in the Basantgarh area of Udhampur district, Indian troops shot dead a fighter who was later identified by them as Abu Bilal Afghani - a member of Lashkar-e-Tayaba, a pan-Islamic group fighting Indian rule in Kashmir.
The surge in violence occurred on a day India's army chief General JJ Singh was visiting the valley.
Exchange of high-level officials
has warmed relations
After being briefed by military officials on the progress of work on the stretch of a road that links Srinagar with Muzaffarabad, the capital of Pakistan-administered-Kashmir, Singh flew over the Line of Control (LoC) fence to take stock of the situation along the de facto border.
The LoC splits Kashmir between Indian- and Pakistan-controlled parts.
India has erected a 12ft-high fence along the 767km-long border and says the measure has helped it to reduce cross-border activities, including infiltration by armed groups.
A bus service is to connect Srinagar with Muzaffarabad on 17 April as part of several confidence-building measures initiated by India and Pakistan.
Some of the fighting groups have opposed the bus on the grounds that it would dilute the Kashmir issue.