The two victims, both adults, were killed when the vehicle struck several pedestrians and the fireworks stand, police said.
Police believe the man driving the van had a medical emergency before the crash, according to DC Metro Deputy Chief of Police Wilfredo Manlapaz.
At a press conference, Manlapaz said the truck traveling northbound on the street ran through a red light and hit a cyclist on the crosswalk before hitting the fireworks stand.
The cyclist and pit worker were pronounced dead at the scene, he said. The truck driver and a passenger were taken to hospital.
No one else was injured in the incident, and police do not believe the accident caused a firework to explode, Manlapaz said.
It is not known if there was anyone else on the stand at the time of the accident.