The concert, called Safe & Sound, took place on Saturday night in the Hamptons and was billed as a "drive-in music experience".
But video taken from the stage showed crowds of people outside their cars, standing in close proximity.
New York governor Andrew Cuomo said he was "appalled" by the footage.
Announcing an investigation into the concert, Cuomo wrote: "We have no tolerance for the illegal and reckless endangerment of public health".
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