Sekhri, 39, met in London and got married in 2009 and have a two-year-old son.
Ruling on the latest stage of their legal battle at a hearing in the Family Division in London on Thursday, justice Holman described their case as "financial suicide".
"They have each spent the staggering sum of about £430,000 on worldwide legal costs," he said.
"The substantial forensic struggle throughout the hearing was painful to observe. These parties are successful and prosperous but they are not multimillionaires," he added.
He pointed out that the couple had spent nearly a quarter of their combined wealth, estimated at around £4 million, in the pursuit of a divorce.
Sekhri, a paediatric anaesthetist, wanted legal proceedings to be conducted in the UK and issued a divorce petition in London in August 2012.
However, Ray, a partner with US-based law firm White & Case, objected and the legal bills continued to shoot up.
The judge ruled that Sekhri could pursue divorce proceedings in England even though she and her estranged husband were both of Indian origin and currently lived in Singapore.
He said both had been legally "domiciled" in England.
"Somewhere, the husband will have to make fair provision for his wife. They would be wiser to concentrate on that rather than arguing about the jurisdiction of the fight," the judge stressed.
Sekhri moved to the UK from India in her late teens and worked at Great Ormond Street Hospital in London.
She had been hoping to become a consultant at a leading London hospital when her husband was transferred to Singapore.
Ray was born in the UK and raised in Colindale, north west London.
He was educated at both Oxford and Cambridge Universities and practised in New York for four years before meeting his wife.
The court heard that the couple met through an online dating agency in London in December 2008.
"They met through an online dating agency when each was in their mid-thirties. They were already mature people. They were, and are, each highly intelligent, successful professional people. They each felt that what they lacked in their lives was a long-term partner or spouse," judge Holman said.
The couple married in December 2009 and had their son the following year.
However, the arguments flared in 2011 and although their brief marriage had shown "so much promise", divorce became inevitable.
A date for actual divorce proceedings is yet to be set.