Dr. Martin Haulena of the Aquarium says the male porpoise can't swim on its own, so it's being supported in a specially-designed sling that helps it stay afloat.
It's not known what caused the porpoise to become stranded on the rock in Saanich Inlet.
The aquarium says once they've been stranded, porpoises have a poor chance of recovery, especially if they have serious health problems, such as infections or parasites.
However, it says the aquarium has been successful with porpoise calves in the last few years and it's providing the best care possible for the animal.
Haulena says if the porpoise recovers and shows it can forage for food, it will be released back into the wild.