The car flipped on the northbound highway near Merrick Road just after 7 a.m.
Two soldiers who were on their way to help in the administration of the vaccine pulled over to help.
Video showed extensive damage to two of the vehicles and to a wooden guardrail in the center median.
Rescue vehicles were on the scene in addition to police.
It appeared the woman in the car suffered a non-life-threatening injury.
There was no immediate word what led to the crash.
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