Three children were among those who died when the van went off the Bronx River Parkway Sunday afternoon and fell about 100 feet on to a railway yard near the Bronx Zoo.
Police said the vehicle somehow went out of control and struck the median. It then crossed all southbound lanes and crashed through the guardrail.
No one on the ground was injured, WNBC-TV in New York said.
Bronx Borough President Ruben Diaz issued a statement Sunday saying he wanted to discuss the overall safety of the parkway with the appropriate agencies. WNBC said two people were injured in a similar accident in the same area last summer.