It happened on East 12th Street around 4:30 a.m. Wednesday.
Investigators said the four suspects were caught on camera.
Photographs from the police union showed the damage done to the inside of the van.
The suspects are accused of breaking one of the van's windows, then setting the vehicle on fire.
No one was hurt.
Anyone with information is asked to call the NYPD's Crime Stoppers hotline at 1-800-577-TIPS (8477), or for Spanish, 1-888-57-PISTA (74782). You can also submit a tip via their website or on Twitter, @NYPDTips. All calls are kept confidential.
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