Security forces had cordoned the area and launched a search operation in the Redwani area of Kulgam district in south Kashmir around midnight. The official said as the searches were going on, militants fired on the forces, who retaliated.
One of the injured soldiers succumbed at a hospital. He has been identified as Sapper Prakash Jadhav, the official said.
The two militants killed in Kulgam were affiliated to the outlawed Lashkar-e-Taiba. They have been identified as Ajaz Ahmad Makroo and Waris Ahmad Malik, the official said.
"As per police records, both the killed terrorists were wanted by the law for their complicity in a series of terror crimes, including attack on security establishments and civilian atrocities," a police spokesman said.