Edwards filed the lawsuit Tuesday in Kanawha (kuh-NAW) County Circuit Court.
He was running full speed for a long pass when his right shin crashed into the cart just beyond the end zone.
The lawsuit says Marshall has a duty to maintain its football field in a reasonably safe manner, including the removal of obstructions.
Edwards missed the remainder of the 2008 season but returned to catch 85 passes for 1,021 yards in 2009.
Marshall spokesman Matt Turner and Conference USA assistant commissioner Courtney Morrison Archer didn't immediately return telephone messages.