The French leader this month declared war on "Islamist separatism", which he believes is taking over some Muslim communities in France.
The Sun newspaper alleged Pogba, a practising Muslim, reacted to Macron's comments by quitting the national team.
The newspaper has since apologised and amended its story.
"Unacceptable," the 27-year-old wrote on an Instagram post along with a "fake news" sticker on a screenshot of the headline from The Sun.
"So The Sun did it again," he added. "Absolutely 100% unfounded news about me are going around, stating things I have never said or thought.
— Paul Pogba (@paulpogba) October 26, 2020"I am appalled, angry, shocked and frustrated some 'media' sources use me to make total fake headlines in the sensible subject of French current events and adding the French national team to the pot.
"I am against any and all forms of terror and violence. Unfortunately, some press people don't act responsibly when writing the news, abusing their press freedom, not verifying if what they write/reproduce is true, creating a gossip chain without caring (if) it affects people's lives and my life."
Pogba added he was taking legal action against the publishers, while The Sun has issued an apology.
A spokesperson for The Sun said: "We reported on a story that Paul Pogba had taken the decision to quit the French national football team after it was published on a sports website.
"That story was also published on The Mirror, Mail Online and other websites.
"Subsequently, Paul Pogba has denied the claim and we have updated our story accordingly.
"We apologise for any upset caused."
The report came days after Macron paid tribute to a French history teacher who was murdered for using cartoons of the Prophet Muhammad in a class on freedom of expression for 13-year-olds.