Investigations have begun to determine whether the soldier was under stress.
A number of Indian soldiers and policemen deployed in the disputed state have been killed in similar incidents in the past.
Stress has been blamed for more than 70 deaths in shooting incidents in India's armed forces since 2001.
Many members of the security forces are denied leave for long periods during tough counter-insurgency operations.
A junior officer was among the four soldiers killed in Anantnag early on Thursday.
One report said that the soldier who shot his colleagues had an altercation with them before the incident.
In January, India's government announced plans to reduce the number of security forces in Indian-administered Kashmir by a quarter .
There are estimated to be between 300,000 and half a million Indian troops and police in Jammu and Kashmir, fighting a two-decades-old insurgency.
India's government has never released official figures on its forces in the region.