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.
A dog has died after falling into the River North Esk in Angus despite a major rescue effort to save the animal.