She cited the alleged war crimes by Sri Lankan defence forces as they defeated the rebel LTTE in 2009, ending the island's lengthy civil war.
"Sri Lanka's participation would hurt people's sentiments in Tamil Nadu," she said, adding that the Union government has ignored a request by her to ban Sri Lanka from the Championships.
The 20th edition of the Championships was to be hosted in India after a gap of nearly 20 years. New Delhi had hosted it in 1989.
Yesterday, the chief minister described as "a war crime" the alleged execution of the 12-year- old son of LTTE chief V Prabhakaran.
Photos released by UK's Channel 4 show the child snacking while in military custody just hours before he was shot dead. The photos, which are morphed according to the Sri Lanka administration, feature in a new documentary that will screen next month in Geneva to coincide with a UN Human Rights Council discussion on the country, currently facing censure by the US over its failure to probe war crimes.
The DMK, a senior ally in the Prime Minister's ruling coalition, has said that India must vote against Sri Lanka and support the resolution.
Last year, after the party threatened to quit the government, India voted against Sri Lanka as the UN's top human rights body asked the island to look into allegedly vast human rights violations as the defence forces defeated the rebel Tigers.
Rights groups say up to 40,000 civilians were killed by security forces.
The Sri Lankan government has denied causing civilian deaths and has maintained that LTTE chief Prabhakaran's family were killed in fighting. The bodies of his wife and daughter have not been found.