The Velez Sarsfield v San Lorenzo match was halted when visiting fans broke down the fencing around the pitch and Velez goalkeeper Pablo Migliore was hit by a missile thrown from the crowd.
Referee Sergio Pezzota led the teams off the field and abandoned the match, telling reporters his decision was due to "lack of security."
Media reports said that around 160 San Lorenzo fans clashed with police outside the stadium and that one supporter died from a heart attack.
Other versions said the victim had been kicked by a police horse.
The Velez v San Lorenzo fixture is considered high risk and local authorities have banned the presence of away fans at recent meetings.
However, this was lifted for Sunday's game at the request of the two club presidents.
"Obviously, we made a mistake and the message is that we can't do this," Velez president Fernando Raffaini told the Telam news agency.
"I'm sorry from the bottom of my heart and there are situations which surprise me and leave me speechless."
Almost three years ago to the day, a match between the two at San Lorenzo's stadium was abandoned before kick-off in almost identical circumstances.
A 21-year-old Velez fan was shot dead on his way to the game and when the club's supporters heard the news in the stadium, they broke down the fencing and invaded the pitch.
Argentine football is plagued by violence involving hardcore fans known as "barras bravas."
