Pakistan has won praise from its ally Washington after capturing high-profile Afghan Taliban figures.
The blast left a huge crater in the road outside the office of the FIA, and destroyed the front of the building.
Scenes of destruction
Kamal Hyder, Al Jazeera's correspondent in Pakistan, said the dead included three officials and two school girls.
The FIA has been attacked at least twice before.
Tariq Saleem Dogar, the provincial police chief, told reporters: "According to initial reports, terrorists came in a car and exploded."
Television footage showed scenes of major destruction with fallen masonry, a large crater in the ground and volunteers trying to shift debris by hand as ambulances raced to the scene.
Angry residents shouted at police as they arrived at the scene in Lahore's Model Town residential neighbourhood.
"We repeatedly asked them to please move this office away from our houses but they didn't give a damn," one woman said.
Stock market investors, growing accustomed to bomb attacks across the country, shrugged off the latest violence, dealers said.
"The market has become sort of immune to these acts of terror and it only reacts if the damage is huge," said Khalid Iqbal Siddiqui, director at Brokers Invest and Finance Securities.
Dealers said healthy foreign flows into the market in recent days had helped investor sentiment.