Alexander Bradley, 30, filed his complaint against Hernandez on Wednesday, with the ex-NFL star invoking his Fifth Amendment right, which protects people from incriminating themselves.
NBC Sports reports that Bradley has accused Hernandez of using a gun on him following a disagreement outside the bar earlier this year.
Bradley is seeking upwards of $100,000 (£61,000) in personal damages for the incident.
Hernandez was released by the Patriots in June after he was charged with the murder of 27-year-old Oden Lloyd in Massachusetts.
He maintains his innocence in the killing of Lloyd.