In the video which has been deleted from social media, a man, who looked like the Zenit St Petersburg star, was seen pleasuring himself in the clip.
The video went viral in Russia on Saturday after it was leaked online.
Dzyuba, became a star in his country after scoring three times at the 2018 World Cup.
He has now been left out of the Russia team and the team manager Cherchesov has now explained the decision.
He said: “The situation with Artem Dzyuba has nothing to do with the Russian national team from a sports point of view.
“Therefore, we see no need to give detailed evaluative comments on this matter.
“However, the coaching staff of the national team understands very well that the national team should prepare for the November matches with Moldova, Turkey and Serbia in conditions of maximum concentration and not be distracted by extraneous things.
“We have always emphasised that everyone, both on and off the football field, must correspond to the level and status of a player in the national team.
“In this regard, today it was decided not to call Artem Dzyuba to the current training camp in order to protect both the team and the football player from excessive negativity and stress. Dzyuba will have time to normalise the situation.
“I hope that this topic will no longer be raised during the team’s work at this training camp.”