An officer in the city of Recife said the clash happened at the Arruda stadium after a match between Santa Cruz and Parana.
He said fans ripped three toilet bowls out of stadium lavatories and threw them from the stands. He said one hit and instantly killed a supporter, who was named as Paulo Ricardo Gomes da Silva.
The incident comes six weeks before Brazil hosts the World Cup. Four tournament games are being played in Recife.