Three of the South Australian's Rajasthan Royals team-mates were questioned by police on Thursday following allegations of spot-fixing in the Twenty20 tournament.
Rumours then emerged via social media regarding Tait, prompting Australian cricket's governing body to come out in strong defence of the paceman.
"Shaun reiterated to CA that he had absolutely no involvement in any of the issues that are currently being investigated," the statement read.
"CA is comfortable that Shaun is being appropriately supported in India and reminds those who have been speculating on the ongoing investigations to base their comments on known facts, not unsubstantiated rumour."
The head of CA's anti-corruption unit Sean Carroll confirmed he had spoken to Tait, and he is not involved in Delhi Police's investigations into the Royals trio.
Tait also released a statement previously through his management, explaining he had undergone significant emotional trauma.
"I'm bewildered, I'm angry and I'm upset at the false suggestions I've been involved in any wrongdoing," the statement read.
"While I welcome the recent statements from police clearing me of any involvement, for a few hours today I was deeply distressed by the rumours that were rapidly circulating about me, most of which were aired in the social media space.
"Not only were they without foundation, they highlight the danger of a medium that deals with innuendo rather than fact, the result of which has brought my name into question.
"At no stage in my career have I engaged in spot- or match-fixing and I'm in discussions with my manager and legal representatives to examine how this episode unfolded and any further action I may take.
"I pride myself on playing cricket hard and fair and look forward to continuing my career in this vein."