The Taliban has sealed off the area and was retrieving bodies from the rubble of the building, officials said.
Kurram is a known hub for fighters loyal to Baitullah Mehsud, Pakistan's most wanted man, and Sirajuddin Haqqani, de facto commander of Taliban-aligned groups on the border.
Security officials had earlier said that at least seven fighters had been killed in the attack, including "foreigners" - using a term adopted to mean al-Qaeda operatives.
More than 30 such missile attacks have been carried out since August 2008, one month before Asif Ali Zardari was sworn into office as president of Pakistan, killing more than 320 people.
The US military does not confirm drone attacks, but it and the Central Intelligence Agency operating in Afghanistan are the only forces to deploy drones in the region.
It was the fifth missile attack blamed on unmanned US aircraft since Barack Obama, the US president, came to power, dashing the Pakistani public's hopes that the new administration would abandon the policy.
Obama says fighters in Pakistan and Afghanistan, where US troops are battling the Taliban, pose a grave threat.
Islamabad has repeatedly protested to Washington that drones violate its territorial sovereignty and deepen resentment among the 160 million people of the nuclear-armed Islamic nation.