The four-storey structure in the capital Srinagar was in flames after a five-hour battle between soldiers and fighters, security force spokesman T Acharya said.
He said one fighter was killed as he jumped from the first floor to escape, while one more was trapped inside.
Two soldiers were wounded when the fighters threw grenades and fired at a security detail guarding the building where the information departments for the federal government and Jammu and Kashmir state are located.
Three others were wounded in the gun battle that followed.
Witnesses said an adjoining building, which has the offices of three Urdu-language dailies, also caught fire.
Security forces evacuated a dozen families from nearby buildings in Lal Chowk, a buzzing business centre in Srinagar.
Al-Mansurin, a separatist group that has claimed responsibility for several attacks in the past, said it had carried out Tuesday's attack.
In a message to local newspapers, the group said it had launched the attack because the state's governor said on Monday that such attacks had stopped in the Kashmir valley.
Elsewhere five people including two fighters and a soldier were killed in separate shootouts in the disputed Himalayan region.