Nathan Marlowe and his wife Cynthia Manzo say Simmons attacked them, threatened them and took their video camera at The Grove mall on Saturday after they were filming him.
The complaint says Marlowe asked Simmons for his view on monogamy, and Simmons then told him to get his shot and leave.
The rocker then allegedly lunged at Marlowe, taking the video camera. He turned on Manzo, the couple says, when she tried to get the camera back.
The couple is seeking damages of more than $25,000 for civil claims of assault, battery and infliction of emotional distress.
The couple also sought a restraining order against Simmons on Wednesday, but that was denied.
Simmons has not been arrested and no charges have been filed.