"The French Professional League has decided to open an investigation following Taye Taiwo's behaviour after the League Cup Final between Olympique Marseille and Montpellier," the LFP said in a statement on Sunday.
Taiwo scored Marseille's goal in their 1-0 defeat of Montpellier at the Stade de France on Saturday.
After the team were presented with the trophy, he took a microphone and sang, along with fans, a song aimed at arch-rivals PSG.
"The League will hand the file to the (French federation's) Ethics Committee," the LFP added.
Asked what he thought of the incident on Saturday, Deschamps replied: "I did not hear it. It will give you something to write about.
"The less you write about it, the better it is."
Taiwo told OM's website on Sunday that he was sorry for his actions.
"I want to apologise for what I have sung at the Stade de France," he said.
"All my team mates told me it was not a good thing to do and that it hurt their feelings. I now also feel bad to have done that.
"I was euphoric, we had just won and we were singing... Once again, I apologise."
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