Media reports said that shots were fired into the air by security guards and the club said it would investigate, although it added that none of its employees carried guns.
Television pictures showed around 30 supporters running onto the field as the players were training.
One man was seen to aim a punch at midfielder Diguinho who hit back and tried to escape through a side door. Reports said fans retreated after a security guard fired two shots into the air.
The players went inside and later continued the practice under a police guard while fans continued to argue with club officials.
The protest followed home defeats against Corinthians and Santos by Fluminense who are led by former Brazil and South Africa coach Carlos Alberto Parreira.
The fans had begun their protest by standing on the terraces and chanting insults at the players as they jogged around the field during a warm-up.
Club official Marcelo Penha promised extra security.
"We understand that Fluminense supporters are not satisfied with recent results but we will not accept, under any circumstances, the acts of vandalism that were carried out today," he said.
"It's unacceptable that the players are attacked by vandals, especially at their place of work."
He denied that the club security guards were armed. "We will find out if there were really shots and we will punish the culprit if necessary."
'People will remember us because we got to No.1 in the world rankings and achieved great things - but our biggest regret is that we didn’t win anything': Ex-Everton star Kevin Mirallas opens up on 'honour' of being part of nation's golden generation
‘I’m sure we’d have finished in the top four or five if he hadn’t joined Chelsea in January. Him leaving damaged the team, but we couldn’t stand in his way’: Alan Curbishley reflects on failed Champions League dream after selling key player
