Richard Huntington, chairman of global firm Saatchi & Saatchi, and wife Annabel Bird, who runs the luxury lifestyle brand Bleak House, launched a GoFundMe page with the aim of raising £7,500 (AU$13,000).
The couple made the request when they discovered their Insta-famous dog, Edward Lear – who has over 10,000 followers – was suffering from "elbow dysplasia in his front leg and also had torn cruciate ligaments in two of his rear legs."
The British couple said that the money raised would pay for the dog to have a total of three operations with celebrity vet Noel Fitzpatrick, star of British TV show Supervet.
In the public plea, Annabel stated that their insurer would not cover the cost of the treatment as it was deemed to be a pre existing condition
"So, we are left with bills of £7,500 and are asking for help to pay them," the page reads.
"Both Richard (Edward's dog-dad) and I would be so incredibly grateful for any help you can give us with our vet bills.
"We will be posting daily updates on instagram and here as well so that you can see how he is doing."
Donations have since flooded in with the total amount raised standing at more than £5,300 (AU$9,250).
Mr Huntington was appointed Chief Strategy Officer for global ad agency Saatchi & Saatchi last year and is thought to command a six-figure salary.
The couple, who live in a house worth more than £1m (AU$1.7M) in an affluent North London suburb, were slammed on Twitter, with one user writing: "A tale of utter shamelessness" after the story emerged in Private Eye.
However, Mr Huntington told Private Eye that he had been inundated with support. His wife has also defended the campaign.
Responding to the criticism of the appeal, Annabel wrote on the crowdfunding page: “Thank you again to everyone who contributed to Edward’s GoFundMe. Unfortunately, his page has received some negative press because of who my husband Richard works for.
“As you know, this page was set up for our friends and family and those of mine and Edward’s Instagram followers who kindly asked to donate money to help with his recovery. This is not uncommon in the dog community on Instagram which is a wholly supportive and wonderful place to hang out.”