Directing the government to produce the documents before September 9, the bench said a detailed hearing in the matter will be held on September 15.
In its application, the state government said unless the stay is granted, it will be put to irreparable injury and hardship.
The state government filed the application in the court, after an all-party-meeting in the state demanded withdrawal of the Union Cabinet's decision last week to lease out the airport to Adani Enterprises.
Last year, the high court had dismissed the petition challenging the decision, terming it as not maintainable under Article 226 of the Constitution.
The state government then filed an appeal before the Supreme Court against the high court order.
The apex court set aside the judgement of the high court and the matter was remanded back to it for a decision on merit.
Referring to the top court directive, the state government said, "all further proceedings in relation to grant of lease with regard to operation, management and development of Thiruvananthapuram international airport to Adani Enterprises Ltd, is to be stayed pending disposal of the aforementioned writ petition."
This story has been published from a wire agency feed without modifications to the text. Only the headline has been changed.