Crighton Pet Services said the animal died after consuming poison in Campbell Park in the Colinton Area.
It posted a warning on Facebook saying: "Please be aware that we’ve had reports of a dog being poisoned at Campbell Park in Colinton.
"Tragically, the dog died.
"This was originally reported as rat poison laid by the council - however, another dog walker contacted the council and they have said that their rodent poison is encased to prevent the wrong animals getting to it and it’s unlikely this was the cause. They are investigating the matter further."
"Please whatever you do avoid that park or at least don’t let your dogs run round the edges of the park or where the big container is!"
The post has been shared over 200 times.
One dog owner has since commented: "I’m going to start muzzling my dog for his own safety.
"It’s absolutely shameful that people could do this."
A spokeswoman from Edinburgh City Council said: "“We are aware of the matter and are currently investigating the area.”