Jayalalithaa's action came two days after the team from Royal College, Colombo, played a match against Customs Department.
She said she has directed Chief Secretary Debendranath Sarangi to suspend an official in the Nehru Stadium of the state government for giving oral approval for the match and initiate department level proceedings against him.
"The (Nehru) Stadium officer has no authority to allow matches there and only the Sports Development Authority of Tamil Nadu is authorised to do so. By using an authority that did not exist, the official had demeaned the sentiments of Tamil people," she said in a statement.
"I have also instructed that no competition must be held for the Sri Lankan team besides directing that they be sent back," Jayalalithaa said.
Her action come against the backdrop of her consistent opposition to India training Lankan military personnel, saying the island republic's forces had committed war crimes against Tamils.
Jayalalithaa also slammed the Centre for allowing the Sri Lankan football team play matches in Tamil Nadu.
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She said she had received information that an official of Royal College of Colombo had called up an officer at Reserve Bank of India in Chennai seeking arrangements for some Lankan football players to play friendly ties here.
The team played the match on August 31 and coming to know about this, she said, she had directed a complete probe.
Jayalalithaa said she had also directed eight students of a Sri Lankan school who had come for a tournament with a city-based school and their coach to be sent back.
The Chief Minister criticised the Centre for allowing the Sri Lankan football team to land in India despite paying no heed to her earlier pleas that included imposing sanctions on Sri Lanka till Tamils in the camps were rehabilitated on par with majority Sinhalese.