The 49-year-old was sacked following his team's surprise defeat by Wales in the quarter-finals of the tournament.
"Wilmots - not for the first time - reiterates publicly and intentionally accusations against my honour and reputation as well as my father," Courtois said on social media.
"We decided together to file a complaint accompanied by criminal indemnification proceedings for libel and defamation."
Courtois and Wilmots also had a public falling out with the goalkeeper criticising Belgium's tactics during the Euro 2016.
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
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