Other Uruguayan players are also said to have been involved in the incident.
Uruguay captain Jose Maria Jimenez said the players were trying to protect their families and described the situation in the crowd as a “catastrophe”, Reuters reported.
He continued: “There was no police and we had to protect our families. It was the fault of two or three people who drank too much and didn't know how to drink.”
The incident comes after Uruguay lost 1-0 to Colombia in their last four games, ending their hopes of reaching the Copa America final on Monday.
Just before the crowd chaos began, players and coaching staff clashed on the pitch after the game.
Nunez started as a striker for Uruguay but failed to convert any of his four shots on goal.
Liverpool signed the forward from Portuguese side Benfica for an initial fee of £64m in June 2022. He has scored 20 goals in 65 appearances for the club.
BBC News has reached out to Nunez's spokesperson for comment.
Colombia will play Argentina in the final on Monday.
