A report in The Australian said orders handed by the New South Wales Supreme Court prevented the newspaper from using or disclosing the content of any of the documents, and also requires it to remove the leaked documents from its website.
The restriction expires at 5 p.m. on Thursday.
However, the court has also asked the newspaper to hand over, to DCNS, all of the company material in its possession.
Cameon Stewart, the journalist who broke the story, in response to an email from IANS on Tuesday, said the newspaper will hand over the documents that are on The Australian's website.
"We will hand over those few documents which we have a placed on the web in redacted form," Stewart told IANS.
Asked what will be the newspaper's line of action once the temporary order ends on Thursday evening, he said: "I can't answer this until after the court proceedings."
Stewart had told IANS on Friday that the newspaper did not intend to publish any more of the documents at that time.
In a series of tweets later he claimed the documents contained information on weapon systems as well, and said it would be published on Monday.
The newspaper has not uploaded any fresh leaked documents since Thursday, though in a report on Sunday, it had said the leaked documents include details of the capabilities of the SM.39 anti-ship missile expected to be used on the Indian submarines.
An affidavit filed by DCNS says the disclosure of the material has caused a prejudice to the shipbuilder because its competitors now have access to some of the company's material.
"The publication of this highly valuable document causes a direct harm to DCNS and its customer in terms of spread of sensitive and restricted information, image and reputation," said an affidavit by DCNS' lawyer Justine Munsie.
The massive media coverage of the leak had jeopardised the company's international image and reputation, the affidavit said.
"The sensitive and protected nature of the documents also covers the nature, structure and the mere existence of the documents themselves," it said.
DCNS, which is at the centre of a global submarine data leak scandal, wanted to prevent The Australian from releasing any more confidential data contained in the leaked 22,400 secret documents because it may cause harm to its customer -- the Indian Navy.
In response to an email from IANS on Monday, DCNS' Media Relations head Emmanuel Gaudez said: "To be precise, DCNS is instructing a demand to The Australian in order to remove from its website the documents which it has published online and prevent the publishing of other documents."
The Australian has redacted the most sensitive details from the documents before their publication.
The Indian Navy has maintained the leaked data will not compromise the boat's stealth capabilities, and an officer told IANS that, if needed, India is capable of making suitable changes in the submarines keeping in mind the "worst-case scenario".
Navy Chief Admiral Sunil Lanba on Monday had said the Indian Navy is taking it "very seriously" and that "mitigation measures" will be taken based on the report of a probe panel.
