TV footage showed Benzema telling full-back Ferland Mendy: "He does what he wants. Don't pass to him, brother. He is playing against us," in words allegedly aimed at Vinicius at half-time in Madrid's Champions League game with Borussia Monchengladbach.
Reports in Spain have suggested that Benzema spoke to Vinicius in Thursday's training session to resolve the matter.
"The most important thing is it has been cleared up. The players spoke among themselves," Zidane said in a news conference on Friday. "It's no problem.
"A lot of things are said on the pitch and it stays there. We are a team, we need our energy for other things. It's good sometimes, when these things happen, it means we're alive. They spoke and it's all perfect.
"There's no problem, quite the opposite. It happens a lot on the pitch. I'm not saying that to hide anything. It's natural. Afterwards the players talk between themselves, and the next day it's all forgotten. I know the public and the press like these things, but it happens a lot, in the heat of the moment. It shows the character of the team."
Sources close to Vinicius had expressed their surprise at Benzema's comments, telling ESPN that the Brazil international enjoys playing with the centre-forward and looks up to him.
Coach Zidane denied that the French striker's image could be affected by the row.
"I don't think so. Things happen on the pitch, and it stays there," he said. "Nowadays the problem is we have a lot more cameras than before. That has changed, but this has always happened between players."
Sources close to the Real Madrid dressing room told ESPN this week that there is some frustration among teammates and coaches about Vinicius' decision-making in the final third -- although they believe that will improve with time.
The 20-year-old has scored three goals in seven matches so far this season.
"He is young. He has a present and a future at Real Madrid," Zidane said. "He is working hard. He's a boy who wants to learn and improve. That's good for a coach and a team."
Zidane -- who had a reputation for a fiery temper as a player -- said that he was frequently involved in heated discussions himself.
"It has always happened," he said. "You say something to a teammate in the heat of the moment. And it wasn't just me saying it about others. They said things about me too!"