Animal-lovers who have been demanding better medical care for the elephant now say there is little hope of any improvement in her condition.
Forest officials said they managed to pull her out of the swamp with great effort, but vets later said her fracture could not be repaired, and she would never be able to stand again.
As her condition worsened, many in the city of Dehradun said prayers while a team of three vets declared it was better to kill her.
Just as her life was due to end last Saturday, an animal campaigning group - Peoples For Animals (PFA) - made an 11th hour appeal to the authorities against the lethal injection, prompting them to defer a decision.
"We will go to the courts," said PFA spokeswoman Puja Bhaukhand.
"Forest officials are responsible for Arundhati's condition as they failed to provide her adequate medical care."
The Chief Wildlife Warden of Uttarakhand state, Shrikant Chandola, told the Indian Express newspaper he had signed the approval to kill her by injection "with a heavy heart".
Maneka Gandhi, a former Indian environment minister and animal rights campaigner, agreed with Mr Chandola that it was too late to do anything to save Arundhati.
"At this point mercy killing is the only option left," she told the BBC.
'Medical negligence'
But Ms Gandhi also expressed concern at the lack of medical care for wildlife in India.
"There was a delay in providing proper medicines and care to the elephant," she said.
"The point is we will not learn any lessons from this. The same mistake will be repeated."
Ms Gandhi said medical experts should be employed to protect wild animals and medical negligence of such animals should be made a punishable offence.
Arundhati was barely six months old when she separated from a herd of wild elephants and found her way into the Rajaji National Park, reputedly the largest abode of Asiatic elephants.
Trained by elephant riders known as
mahouts
, she became a major visitors' attraction, often giving them rides or simply playing with small children.
Her
mahout
, Zahoor Khan, has been in tears at the thought of parting with her.
But prayers, protests and even traditional medicines have so far failed to revive her.
Reports say it is simply a matter of time before the lethal injection is administered.
