Lt-Col JS Brar said three soldiers had been injured in the violence, which was ongoing.
Fighting began after a woman who was being held hostage there sneaked out.
Kashmir, which is claimed by both India and Pakistan, has recently seen a drop in violence.
Thousands of people have been killed in the region since an armed rebellion against Indian rule erupted in 1989.
The operation in Kupwara was launched early on Friday after the army received information that some militants were holding a meeting in the house, Lt-Col Brar said.
Security forces began firing after the woman emerged from the house, officials said.
Residents had been asked to leave the area, reports said.