The apex court asked the Tamil Nadu government and Vedanta to approach Madras High Court on the issue.
A bench headed by Justice Rohinton Fali Nariman set aside NGT's order on grounds that the plea of Vedanta before the tribunal was not maintainable.
The apex court said NGT did not have jurisdiction to entertain Vedanta's appeals against the Tamil Nadu government to close down the Sterlite plant.
The Tamil Nadu government in its appeal against the NGT order had sought that the tribunal order be set aside on grounds of it being "erroneous".
The tribunal failed to consider the data, documents, and evidence furnished by the Tamil Nadu Pollution Control Board to show that Vedanta had irreversibly polluted the groundwater in and around Thoothukudi district, the government has contended.
The state government had closed Vedanta's Copper plant six days after 13 people were killed in police firing against people who were protesting against the plant on grounds that it polluted the environment.
Vedanta had also approached the apex court accusing the Tamil Nadu government of delaying implementation of NGT's order that allowed its Thoothukudi plant to reopen.