Melati, 10, died on Friday during her first meeting with seven-year-old Asim - whose name means "protector" in Arabic.
They had been housed in adjoining enclosures for the last 10 days so they could see and smell each other, and it was hoped they would breed as part of a Europe-wide conservation programme for the species.
But the zoo said their first encounter "quickly escalated into a more aggressive interaction".
Keepers tried to separate the tigers using flares and alarms, but they could not save Melati.
In a statement, the zoo said staff are "devastated by the loss of Melati, and we are heartbroken by this turn of events".
When Asim arrived at the zoo from Denmark at the end of last month, he was described as "strapping".
Head tiger keeper Kathryn Sanders said at the time that he had "made himself at home in his new, cosy den".
She said: "Asim is a handsome, confident cat who is known for being very affectionate with the ladies in his life - we're hoping he'll be the perfect mate for our beautiful Melati."
Keepers had chosen Asim after meeting him and assessing his personality, explaining: "We learned that he adores chicken and loves to play, particularly by pouncing on piles of empty boxes sprayed with strong scents such as herbs and spices."
And in the hope of a successful union, shortly after Asim arrived at London Zoo, they had said: "It's early days but we've already seen some good signs - there has been lots of 'chuffing' which is a happy sound they make to let each other know they have good intentions. It's fantastic to see that they're interested in each other already."
London Zoo says its tiger territory will remain closed while the team focus on caring for Asim.
The World Wildlife Federation says Sumatran tigers are critically endangered and there are thought to be fewer than 400 left in the wild.