The 28-year-old man died after being hit by bullets in his chest during the disturbances which took place ahead of Sunday's game in the Nilton Santos Stadium, which six months ago hosted Olympic track and field events.
One of the seven people injured was in serious condition, police said.
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According to initial police reports, the shots were fired from a vehicle.
Police stations in Rio have been disrupted since last week by family members demanding better conditions for officers.
Despite assurances that the demonstrations -- which have partially blockaded several stations -- have not hindered policing, authorities said Monday that the unrest "had an impact" on security Sunday.
Reports in the Brazilian media said that police numbers were far lower than necessary for the event.
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