"I confirm that there is one person dead. This person died of cardiac arrest," said Security Minister for the province of Buenos Aires, Sergio Berni.
The hospital where the victim was taken said he was a 57-year-old man who died of cardiac arrest.
The clashes began outside the Juan Carmelo Zerillo stadium in La Plata, about 50 kilometers south of Buenos Aires, where Gimnasia were playing Boca Juniors.
Police used rubber bullets and tear gas to disperse supporters who tried to enter the already sold-out stadium.
"The incidents started outside and spread to the inside. There were about ten thousand people around the stadium trying to get in, some with tickets, others without tickets. Everyone could see that the stadium was very full", said Eduardo Aparício, the head of the body for the prevention of violence in sport.