Local administrative and intelligence officials also said that the death toll, which included two women, may yet rise.
"Today's incident was a result of sectarian violence," Major Fazal-Ur-Rehman, a spokesman for the paramilitary frontier corps, said.
Security officials said more troops have been deployed to guard the route.
"Forces do react to the situation and more troops have been deployed for the route protection," the senior security official based in Peshawar told the AFP news agency.
The road linking Kurram with Peshawar often has to close due to attacks from fighters and Pakistan army operations, forcing people to take a circuitous route through Afghanistan to travel to the Khyber-Pakhtunkhwa province and its capital, Peshawar.
However, that route is not safe either. At least 11 people were killed in a similar attack last week when a passenger bus heading to Peshawar was attacked inside Afghanistan.
The attacks have led to civilian convoys increasingly asking for security to protect them.
Kurram has seen escalating violence over the last few years, like most of Pakistan's federally administered tribal agencies.
Dozens of people were kidnapped there in May, and fighting between armed groups and government security forces is common.
The Pakistani army conducted a major offensive in Kurram over the last few months, and recently declared the area largely cleared of tribal fighters.