The blast occurred shortly before noon near the administration block of the sprawling Jalozai camp, which houses both Afghan refugees and people displaced by recent fighting in the northwest.
Noor Akbar, the official in-charge of the camp, told reporters that 12 people were killed.
Two women and as many children were among the dead, officials said.
Officials at a nearby hospital said they had received 35 injured.
Those in a serious condition were sent to Peshawar, the capital of Khyber-Pakhtunkhwa province.
The blast, which was heard from several kilometres away, went off at a time when a large number of people had gathered in the area to register themselves or to collect rations distributed by relief organisations.
Officials said the explosive device was hidden in a car parked in the area.
The blast destroyed several vehicles.
Officials of the bomb disposal squad said an estimated 35 kg of explosives were used in the attack.
No group claimed responsibility for the attack.
Pakistan's northwest has witnessed a spike in militant violence ahead of the general election scheduled to be held on May 11.
The banned Tehrik-e-Taliban Pakistan recently suspended its offer for peace talks with the government and warned it would attack several political parties during the election campaign, including the Pakistan Peoples Party.