As many as five attackers, each wearing belts of explosives, are believed to have been inside the vehicle.
Two died inside the van, while the other three exchanged fire with soldiers before blowing themselves up, according to security officials.
Twelve bodies are reported to have been recovered, most of them civilians.
At least 36 were wounded, among them patients at the nearby Medical City Hospital who suffered fractures from falling masonry.
Sunday's explosion is the biggest to hit Baghdad since.
It comes five days after US forces officially ended their combat mission in Iraq.