Sasha-Lou, an eight-year-old Doberman, suffered a fractured pelvis that was so badly damaged it crushed her spinal cord in the incident on Tuesday night.
Vets who treated the badly injured animal advised his owners, Craig and Sara Price, to put him to sleep just over an hour later.
The loss of their dog has devastated the couple and their daughters, Porsha (15) and Charley-Rai, 12, and they are keen to find the riders involved after they drove off without stopping.
Sara told the Melton Times: “We are devastated and heartbroken that this has happened.
“Sasha-Lou was part of our family.
“She was the sweetest thing you could ever wish to meet.”
Craig was walking Sasha-Lou and another of their dogs on the Viking Way near their home in Sewstern when two motocross bikes drove towards them with the riders apparently racing.
They plowed Sasha-Lou and sent her rolling in a huge puddle in obvious agony.
“She was screaming in pain so loudly that another lady who was walking her dog on a side road in the village heard her,” said Sara, who is a local community nurse.
“My husband went to see our dog and the two riders left.
“If they had just stopped and asked if we needed help it wouldn’t have been so bad, but they left and left her screaming in pain.
“It was very dangerous to cycle there and next time it could be a child who got hit.”
An online fundraising page has raised over £1,000 in just hours to pay the family’s vet bills at Kings in Melton.
The vet waived his professional fees, but the money paid for other costs such as X-rays.
Dozens of others sent messages of sympathy after Sara highlighted the incident on social media.
A local funeral director offered to provide a casket and memorial plaque for Sasha-Lou and a local woman offered to paint it.
Sara added: ‘The help and support from the people of Melton since this has happened has been absolutely overwhelming.
Sarah Mullarkey, who set up the JustGiving page, said: “I don’t know Sara personally, but the story broke my heart.
“It warms my heart that we can help him at this sad time.”
Police recently announced they were stepping up patrols on the Viking Way after reports of motorbikes driving illegally on the road, which is reserved for walkers and riders.
Officers are investigating the incident – contact Pcso 6541 Gray if you have any information on those involved, quoting incident number 131821.