The incident, in which one fan put a gun to a player's head, occurred after evening training on Friday for Saturday's Nacional B championship match against Olimpo.
Salvador D'Antonio, president of the club of the capital's Italian community, complained at the impunity with which "barrabravas" (hooligans) act in Argentine football.
"I've been at this club for 15 years and I've never had a problem like this before. The hooligans have no idea what is it to earn your bread grafting every day, there is total impunity and they take advantage of that," D'Antonio told the sports daily Ole.
Sportivo Italiano's ground is only 500 metres from the Argentine Football Association's training complex on the outskirts of Buenos Aires where coach Diego Maradona is conducting his World Cup preparations.
The players, who told reporters they were shocked when the supporter put his gun to striker Gustavo Britos's head, were meeting players' union general secretary Sergio Marchi on Saturday to discuss what steps to take.
Earlier in the week, coach Mauro Navas of first division Chacarita Juniors, noted for their violent fans, almost resigned when supporters threatened him and his team after two successive defeats. He said he would quit if it happened again.
Argentine football is plagued by the "barrabravas" who exert a strong hold over clubs and players with threats if their wishes are not met.
Club officials and players rarely dare to confront the hooligans and directors keep them onside by providing them with match tickets, transport to away games and freedom to control ventures around stadiums like parking and food stands.
Football violence, which in recent years has centred largely around turf wars between rival gangs of supporters of the same team, has claimed half a dozen lives this year, adding to a total of several hundred.
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