The Parisian team, which currently tops Ligue 1, has backed its defender, calling the "attacks" unacceptable, and say that it will take action if it is deemed necessary.
"These last hours on social networks, unacceptable statements were made by Joey Barton, player of Olympique Marseille against Paris Saint-Germain defender Thiago Silva," a statement on the club's official website read.
"These attacks are serious and go beyond mere verbal joust. The officers of the club, the players and the technical staff supporting Thiago Silva cannot accept such a statement.
"They reiterate their firm commitment to the values of respect that should be the rule of our sport. Thiago Silva and Paris Saint-Germain reserve the right to take any action they deem necessary."
The 30-year-old, currently on loan from QPR, is no stranger to controversy and made comments on Twitter after the Brazil international's press conference in which Silva said that "no one is talking" about Barton and that he did not remember the midfielder's name.
"2 questions for Thiago Silva. Firstly, Why are YOU talking about ME, in your press conference before PSG v Barca? Very strange," Barton wrote.
"Secondly, Are you Pre-Op or Post-Op? #transsexual #thiagosaladyboy... Baffles me, which way he's going. Is he a man changing to a woman or a woman changing to a man? Can't work it out."