Nick Dunn, 28, from Northumberland, was one of six Britons accused of illegally possessing weapons while working on a ship providing anti-piracy protection.
They were arrested in October 2013, but despite the charges being quashed, a police appeal has blocked their return.
Their case was due to be heard later, but has now been adjourned to 22 April.
After the announcement by India's Supreme Court, Nick Dunn's sister, Lisa, said: "This isn't the news we wanted to hear."
Along with Mr Dunn, the men arrested on 12 October 2013 are:
Mr Dunn, who is living in a hostel on the outskirts of Chennai, formally Madras, had said he was "anxious" ahead of the court hearing, which would have been presided over by a judge.
The 28-year-old, from Ashington, said he hoped "that we get the decision we so justly deserve".
Mr Dunn is staying with two Estonians who were also part of the crew of the private US-owned ship MV Seaman Guard Ohio.
Andrew Linnington, of the maritime union Nautilus International, which has been lobbying the UK government on behalf of the crew members, said he feared the six men were being made examples of.
He said: "The Indian authorities want to set a deterrent to operators of similar vessels to the one these six men were working on. Just about every element of this case has been disputed."
A UK Foreign Office spokesman said: "We appreciate that this continues to be a very difficult time for these men and their families and we are committed to keeping them up to date on the latest developments."
He said the prime minister had discussed their case with the with Indian Finance Minister Arun Jaitley and Indian High Commissioner Ranjan Mathai on 14 March.
"We have lobbied regularly on the importance of ensuring that this case is resolved as quickly as possible," he said.
The family of a British man stuck in India, despite being cleared of weapons charges, has expressed disappointment over a delay in his return home.