The alpaca Geronimo, whose fight for life has dominated the UK media in recent weeks after testing positive for bovine tuberculosis, will be put to sleep on Wednesday.
More than 130,000 people signed a petition asking the government to give the animal a reprieve, arguing that the two test results were likely false positive.
Owner Helen Macdonald, who imported Geronimo from New Zealand, sued the government in court to rescue him after losing one last appeal this month.
However, a judge on the High Court in London refused to issue an injunction that would have stopped the execution of the order to destroy the animal.
Judge Mary Stacey concluded that there was “no prospect” that Macdonald would be successful in her attempt to reopen the case.
The government said it would give Macdonald time to arrange the destruction of their pet.
“There are no plans to execute the warrant today,” said a government spokesman.
“We understand Ms. Macdonald’s situation, just as we do with anyone with animals affected by this terrible disease.
“Although no one wants to kill infected animals, we must do everything possible to combat this disease, to stop it from spreading and to protect the livelihoods of those affected.”
Dozens of protesters marched from the Department of Agriculture to Downing Street last week, questioning the accuracy of the positive tests showing Geronimo has bovine TB.
MacDonald has vowed to stand in the way of government-mandated vets who are supposed to carry out the proposed euthanasia, with Geronimo’s plight making headlines in British newspapers for days.
Prime Minister Boris Johnson’s father, Stanley, even got involved, calling the planned killing “absurd” and a “grueling assignment”.
Environment Secretary George Eustice, a former farmer, said he sympathizes with Macdonald, a veterinarian and alpaca breeder who runs a farm in Gloucestershire, western England.
But he claimed the ministry was using a “very specific and reliable test” and that Geronimo had to be euthanized.