The 30-year-old QPR midfielder, on loan in France, made offensive comments about the defender and the Ligue 1 leaders had threatened to "take any action" they deemed necessary
The Parisian team, who currently top Ligue 1, called the "attacks" unacceptable and said that they would take action if deemed necessary.
However, Barton and his adoptive club have apologised for his conduct in a bid to draw a line under the matter.
"L'Olympique de Marseille and Joey Barton wish to apologise to Thiago Silva and his club for the inappropriate statements held by the English player on social networks during the past 36 hours," the statement read.
"This morning, the management asked Olympian Joey Barton to put an end to the controversy which opposed him to the Brazilian defender.
"The Olympian midfielder pledged to immediately cease the posting of any derogatory statements against Thiago Silva."
Barton, 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."