Leaders of various opposition parties have welcomed the court order and also demanded the resignation of Chief Minister E Palaniswami's government.
The court ordered the Central Bureau of Investigation or CBI probe following a petition filed by DMK legislator J Anbazhagan.
The case is related to an Income Tax Department raid in the offices, residences and godowns of a gutka manufacturer in Tamil Nadu in 2016.
A diary was then seized which listed alleged bribe payments made to various officials.
The Tamil Nadu government has banned the manufacture and storage of gutka -- a tobacco product. However, the product was reportedly available in the market with the alleged connivance of police officers and others.
Several political parties had demanded the CBI probe into the scam but the AIADMK government did not agree.
Meanwhile, Tamil Nadu Director General of Police TK Rajendran met Chief Minister Palaniswami, Chief Secretary Girija Vaidyanathan and Home Secretary Niranjan Mardi soon after the court order.
Welcoming the High Court order, PMK leader Anbumani Ramadoss demanded Mr Palaniswami's resignation.
In order to allow the CBI probe to progress smoothly, the Palaniswami government should resign, he said.
Mr Stalin said an English television channel had reported bribes were allegedly paid to top police officials.
Mr Stalin added the issue was raised by him in the state Assembly he and several of his party members were sent out. Speaker P Dhanapal termed it as breach of privilege for bringing a banned substance into the Assembly.
The issue was referred to Privilege Committee which had issued a notice to Mr Stalin and some DMK law makers.
"We had obtained a stay against that notice," Mr Stalin said.
According to Mr Stalin, if the CBI probe should proceed smoothly then Health Minister C Vijaya Baskar, DGP TK Rajendran should resign from their respective posts.
Adding further, Mr Stalin said Chief Minister Palaniswami should quit his post so that people are benefitted.
Similarly, the Communist Party of India's (CPI) Tamil Nadu State Secretary R Mutharasan said the CBI probe should be under the supervision of the High Court.
He also said the minister and other officials alleged to be involved in the scam should quit their posts.
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