It comes five months after he was cleared of murdering Michaela, who was killed while on honeymoon.
The lawsuit is directed against Mauritius' Major Crime Investigation Team (MCIT), police commissioner and the government.
Mr Treebhoowoon and fellow hotel employee Sandip Moneea were arrested by the MCIT the day after 27-year-old Michaela, from Co Tyrone, was murdered in the Legends Resort on January 10, 2011.
They were held for 18 months before they were acquitted of the charges in court.
Now, Mr Treebhoowoon alleges another hotel worker, Raj Theekoy, who was the prosecution's star witness, conspired with police officers and lied in court to implicate him.
Michaela, daughter of Tyrone GAA manager Mickey Harte, was strangled in her hotel room.
Mr Treebhoowoon, a hotel room cleaner, and his supervisor, Mr Moneea, were both charged with her murder.
He claimed a confession he made was beaten out of him by police and a jury unanimously cleared both defendants.
In a letter drafted by his legal team, five senior police officers are accused of gross incompetence and torture.
The letter alleges the MCIT lied by claiming investigators had CCTV and DNA evidence incriminating Mr Treebhoowoon.
The police are accused of failing to carry out a basic inquiry into the killing, with 26 key failures being pinpointed by Mr Treebhoowoon's barrister.
It is claimed Mr Treebhoowoon was "relentlessly tortured and terrorised" into signing a "false confession".
In a further allegation, one of the officers is alleged to have threatened the former hotel worker with a revolver he kept in his sock.
Mr Treebhoowoon also says the Mauritian authorities signed off on a prosecution, even though they knew the case was flimsy.
A new investigation into the circumstances surrounding Michaela's murder -- conducted by different officers -- was launched after the men were acquitted. To date, no other suspects have been charged.
One man, former hotel security guard Dassen Narayanen, still faces charges of conspiracy to commit larceny, in relation to alleged theft from the McAreaveys' room.