He reportedly sustained devastating blows to the head during the melee.
Police chief Fabian Bordon said Nieto was pounced on by a group "including a player from the opposing team, an assistant coach and a hooligan." He later died in hospital.
He was reportedly attacked by hooligans who punched, kicked and hit him with a stone in front of his wife and one-month-old daughter.
The match was abandoned with 15 minutes remaining and with Tiro Federal leading 3-1 after eight players had been sent off by the referee. But violence soon spilled out onto the pitch as rival players and fans clashed.
The non-profit group Salvemos al Football (Let's Save Football) says this is the 15th football-related death this year in Argentina.