American Veterinary Medical Association (AVMA)
Despite many claims that animals will need special eclipse glasses or should be kept indoors during the eclipse, retinal damage during the eclipse is a risk primarily to animals (and people) who will be looking directly at the sun. Animals do not generally stare at the sun, and there’s no reason to suspect that they will during the coming solar eclipse.
If YOU will be looking at the eclipse, by all means, use protective eye wear to avoid retinal damage, but your pets will likely ignore the phenomenon other than possibly reacting the same way they would at dusk. Owners who are concerned about their pets' behavior are encouraged to monitor them while outdoors during the eclipse.