Santa Cruz, based in the northeastern coastal city of Recife, had drawn with visiting Parana when violence erupted outside the ground, Globo's web portal G1 reported.
Fans clashed outside the Arruda stadium, ripping out toilet bowls and throwing them at fans congregated below, fatally injuring one, a police spokesman said.
Globo added three more fans were injured, one seriously.
The violence came just over a month before Brazil hosts the World Cup in 12 cities, including Recife, though matches there will take place at another venue, the Pernambuco Arena.
More From This Section
It will cost more than USD 11 billion to stage the event which the five-times champions last hosted in 1950 on a much smaller scale.
The bill has angered many citizens who say the money spent at new state of the art stadiums, some in cities without a major team, such as Recife itself, would have been better directed towards upgrading poor public services.
Last June, more than a million Brazilians marched nationwide to decry the cost of the Cup and some recent protests, while smaller, have ended in violence.