The crash occurred around 11:30 a.m. as the children walked about two blocks through the busy area, bound for the day care center.
Investigators had conflicting reports about how the crash unfolded. According to one account, the driver got out of the silver van and left the engine running, then it moved. Police later said they believed the van was backing up at the time.
The driver was being questioned by police.
Afterward, a police officer guarded the front entrance to the day care.
"I could see on their faces they were upset," said Liana Flores, whose children attend the day care but were not involved in the crash. "The teachers looked like they were about to break out in tears."
Manhattan Borough President Scott Stringer said the area's "overwhelming amount of truck traffic" has been discussed at community meetings. "This is something that we have worried about for months and months," he said.
The New York Police Department is investigating.