The images of Jaminet come from an Instagram story made by the 20-time international, who came off the bench in France's first Test win over Argentina on Saturday in Mendoza.
"I promise, the first Arab I see on the road, I'll headbutt him," Jaminet is filmed as saying.
Toulon's Jaminet played seven minutes and kicked a penalty as an inexperienced France beat Argentina 28-13 in the opening game of their South American tour.
"The French Rugby Federation condemns comments made by Melvyn Jaminet, in a video broadcast on social media," the FFR said.
"Such comments are totally unacceptable and are contrary to the fundamental values of our sport.
"As a consequence, Melvyn Jaminet has been removed from and has left the France squad currently in Argentina.
"An internal investigation is ongoing to shine a light on these comments, which are of an extreme seriousness and will take the appropriate measures."
Jaminet's club, Toulon, who he originally joined as a boy before spells with Toulouse and Perpignan, also slammed the remarks.
"Following the video of Melvyn Jaminet which has appeared on social media, Toulon condemn the comments made and distance themselves from them," Toulon said.
"An internal investigation is underway."
Following the statements from the FFR and four-time French champions Toulon, Jaminet issued an apology.
"I am deeply sorry and ashamed of my comments," Jaminet said on Instagram.
"Racism, in all its forms, is unacceptable and goes against everything I believe in.
"I understand the FFR's punishment and remain at their disposition to be able to shine a light on this incident."
France have two games remaining of their tour, with a non-capped game against Uruguay on Wednesday in Montevideo and a second Test against Argentina in Buenos Aires on Saturday.
