The pair had to be separated by players and staff at the end of Milan's win against Parma.
Afterwards, both men played down the incident, though Di Canio commented on Sky Italia: "Sergio can't go into a physical fight like this, if there had been no one there it would have been a fight.
"Then you can't go and talk in front of the cameras and say that these are off-court matters. Here it's a serious thing eh..."
Meanwhile, Calabria later said in the aftermath: "These are things that happen on the pitch, it was a misunderstanding between me and the coach. We cleared things up, we didn't understand something about each other and then we sorted things out. It's not the first time it's happened in football. I apologize, it wasn't a good thing.
"There are difficult situations, even private and personal ones that no one knows about. I don't even feel like talking about them too much. I want to end this season in the best possible way for the good of the team, which is what I care about most."
Words and thoughts that echoed Conceicao's statements in his press conference: "I watch the games and listen to them with a lot of passion. There was a bit more adrenaline. There was a game situation that I spoke about with Calabria and there were a few words too many in my opinion.
"For me, all footballers are important, like a family. If I have a son who misbehaves, I tell him. And here it's the same. There's no hypocrisy: we tell each other things like men. True, it wasn't nice, but that's normal in football, we're not in church. We've made things clear."