The blast occurred in Eidgah Vegetable Market in Kurram Agency as people shopped for vegetables, killing at least 21 people and injuring over 50, officials said.
Shahid Khan, an assistant tribal administrator, said the explosion took place when the market was crowded with retailers buying fruits and vegetables from a wholesale shop.
A senior security official said initial reports suggest that the explosives hidden in fruit boxes were triggered by a remote control, at 8:50am, when the market was full of people.
Eyewitnesses said they saw children soaked in blood after the bomb ripped through the market. The official list of the those killed and injured displayed outside the agency headquarter hospital in Parachinar included names of two minors, who were killed in the incident.
"That was our combined work with Shahryar group of Mahsud Taliban," Abu Sufyan, a spokesman for the banned Jhangvi group, wrote in a text message to AP news agency.
This was the fourth attack in recent years in the said market.
Kurram has been the scene of increased militant activities in recent years. The Army carried out a massive operation against extremists there but they still have the capacity to strike.
Iqbal Zafar Jhagra, the provincial governor, told local Geo television that the remnants of militant groups targeted by security forces were trying to show their existence by such attacks.
"Terrorists largely eliminated by our security forces and the remaining will soon meet their fate if we all together rise against them," he said. Parachinar is the administrative headquarters of the agency near the Afghan border.
It is small garrison town developed by the British Army in the foothill of Spin Ghar (White Mountain) in mid-1895. The town's total population is about 40,000 comprising people of different tribes, mostly Shia Muslims.
Local leader Faqir Hussain said all the bodies were brought to a Shia mosque for identification and last rites.