"I have taken the decision to suspend Serge Aurier. Paris Saint-Germain is a very strong institution that cannot be harmed by anybody," PSG president Nasser Al-Khelaifi said in a club statement.
The decision to suspend the 23-year-old defender means he will not play any part in Tuesday's Champions League last 16, first leg against Chelsea at the Parc des Princes.
"I will not let anybody put the club in danger and divert us from our objectives, starting with the game against Chelsea that our supporters are really looking forward to.
"All the energy of the club, the players, the coach and his staff, is focused on this huge match for us and our fans."
The announcement came after Ivory Coast international Aurier was reportedly excluded from training with the squad on Sunday following the appearance of the video.
In it, he appeared to describe Blanc as a "faggot", although he was not actually in shot at the time.
When his friend, a former French youth international, asks him whether or not "Blanc sucks off Zlatan (Ibrahimovic)?", Aurier answers: "Yes, he takes everything, even his balls."
Aurier later apologised, telling Canal Plus and beIN Sports: "What I did was really stupid and inexcusable. I apologise to the coach and the supporters.
"I really regret what happened and accept all consequences. I can only thank Laurent Blanc for all that he has done for me at PSG."
Aurier would have been expected to start against Chelsea after being rested for Saturday's 0-0 draw with Lille in Ligue 1 but now Gregory van der Wiel or Marquinhos will take his place.
The Periscope app allows people to broadcast live videos via their smartphones, which Aurier did as his friend, who was smoking a shisha pipe, asked him questions posed by fans.
Aurier, who was born in the Ivory Coast before being raised in the Paris suburbs, continued to insult his team-mates in an expletive-filled tirade, including Angel di Maria, whom he called a "clown".
When asked which PSG goalkeeper, Salvatore Sirigu or Kevin Trapp, was better, Aurier replied simply that Sirigu was "done".
The right-back has responded that the video was old, but comments on the live feed referencing Valentine's Day suggest that it was posted on Saturday night.
Aurier got himself into trouble in a similar manner just under a year ago.
Last season PSG knocked Chelsea out in the last-16 on away goals, despite a controversial red card for Ibrahimovic.
Aurier was then suspended after repeatedly swearing while insulting referee Bjorn Kuipers in a video he posted on social media.