Scottish Fire and Rescue's water rescue units from Perth and Glenrothes attended the incident under the Gannochy Bridge in Edzell.
Fire crews from Montrose and Forfar also attended the scene after the alarm was raised at about 12:55.
A Scottish Fire and Rescue spokeswoman said the dog's body was later recovered from the water.

Police were called to Nuthurst Park in Moston, Manchester, just before 18:55 BST on Saturday.
Greater Manchester Police said officers responded to reports of a girl being raped and the suspect being chased off by members of the public. A boy was arrested in a nearby shop.
The 16-year-old was remanded to appear at Manchester Youth Court on Monday.
The girl is being supported by specially-trained officers.
GMP added: "We are aware of a lot of local speculation regarding the investigation and we would ask that this please stops to allow the investigation and legal process to continue without prejudice."
A dog has died after falling into the River North Esk in Angus despite a major rescue effort to save the animal.
[NEXT_CONCEPT]
A 16-year-old boy has been charged with the rape of an eight-year-old girl in a park.