The off-spinner, Test cricket's second-highest wicket-taker after Australian Shane Warne, released a public statement after several Indian newspapers and TV channels claimed he was a regular visitor to a dance bar in Mumbai where he was introduced to dancer Tarannum Khan.
Indian police are investigating the dancer's links with bookmakers in Mumbai after income tax officials raided her home and discovered 50,000 dollars in cash.
"These media reports have insinuated my possible involvement in a gambling and match-fixing controversy with which I have no connection," Muralitharan, 33, said in the statement on Friday.
"These allegations are shocking and totally baseless. I have travelled to Mumbai on a few occasions in recent years for official award ceremonies and to attend to family business matters.
"On one occasion, I met (Indian) actor Aditya Pancholi who invited me to dinner. Afterwards, we visited Deepa Bar for approximately one hour before I returned to my hotel.
"Contrary to media speculation, I have never been introduced to and nor do I have any links whatsoever with a woman called Tarannum Khan.
"In addition, this was also the only occasion in my life that I visited this particular bar.
"Reports appearing in recent media reports of my close alliance with this bar or the dancer are therefore total fabrications.
"I have been associated with a match-fixing controversy on the basis that I innocently patronised a bar a few years ago, which I believe is grossly unfair.
"Representing Sri Lanka as a cricketer is a truly great honour and a source of immense personal pride. I have always strived to perform to the very best of my ability and have maintained at all times while doing so the highest ethics of the game.
"It is thus deeply upsetting for my family and I that such wild allegations are now being made. I have therefore spoken to my lawyers and I am taking all necessary steps legally available to me in order to safeguard my reputation and integrity.
"I will not be making any further public statements on this subject," Muralitharan said.
Muralitharan, with 558 Test wickets in 94 matches, is due to play in the second and final Test against Bangladesh starting here on Tuesday.