The defender went into a series of crunching tackles that left three teammates all requiring treatment.
"We expect the player to issue an apology, that is the absolute minimum," Udinese sporting director Nereo Bonato said.
Widespread reports in the Italian media claim Danilo, a defender, went into a series of crunching tackles that left Iraqi international Ali Adnan, Venezuelan forward Adalberto Penaranda and Francesco Lodi all requiring treatment.
Altercations ensued and a training game between players was abandoned twice as Danilo and Lodi argued, prompting coach Gigi Del Neri to lambast his players before sending Danilo for an early shower.
Bonato said Danilo would be issued "a fine", although reports claim this latest incident could see him stripped of the captaincy.
He added: "Before we can take any other action we want to understand what caused this inexplicable behaviour."
It is not the first time Danilo, who joined Udinese from Palmeiras in 2011, has courted controversy.
After being accused of racism while playing in the Brazilian top flight, Danilo admitted publicly he had insulted and spat at Atletico Paranaense defender Manoel.
Danilo also hit the headlines in Italy four years ago after he fought with teammate Michele Pazienza in the tunnel leading to the dressing room.
Udinese sit 15th in Italy's Serie A, 18 points behind leaders and champions Juventus.