The soldier shot dead his colleagues at a camp in Bijbehara town, south of Srinagar, an army spokesman, who asked not to be named, told AFP.
"The soldier was arrested immediately after the dawn shooting during an apparently heated exchange of words," the spokesman said, adding an inquiry had been ordered into the deaths.
It was the second such shooting in just over a month in IHK where a 20-year revolt against Indian rule has left more than 47,000 people dead, according to official figures.
In March, an Indian soldier shot dead a senior colleague.
The killings are part of a string of shootings by Indian soldiers of their comrades over the years that doctors have blamed on stress.
Around 100 Indian soldiers also kill themselves every year in Indian-held Kashmir and the insurgency-racked northeastern states, according to army figures.
The army has set up a helpline and yoga classes to assist soldiers deal with stress issues.
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