Shaw also alleges that Green grabbed his iPhone - which contained images of "significant value" - and tossed it into the ocean.
The incident is somewhat reminiscent of Russell Brand's recent iPhone tanty.
The photographer is seeking unspecified damages in his lawsuit, according to the New York Daily News.
He also claims he has racked up significant medical expenses and suffered "humiliation, mental anguish and emotional and physical distress" after the alleged incident.
Shaw's lawyer Sark Ohanian told The News: "Brian just lost his cool and took it too far. It was completely unnecessary. Our client was in a public area. He has a right to take photographs. He wasn't trespassing.
"Brian threw our client to the ground and tossed him around a bit trying to get the camera. That's when he was injured. He sustained some bruising and a black eye."
Check out TMZ for snaps of the encounter.
Read the full lawsuit here.
"We had to file a lawsuit because they denied it happened. They haven't been cooperative," Ohanian added. "We're not claiming anything tremendous or crazy. But our client was injured."
Neither Fox nor Green's reps have commented on the lawsuit.
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