Basil — Food safety facts
Safe to share · Dogs · full breakdown on the linked food page
A few fresh basil leaves are safe for dogs and cats. Not toxic in normal amounts.
Short answer
No, that's perfectly safe. Fresh basil is non-toxic to dogs in the small amounts typically found in cooking or gardening. It might even add a little fiber to their diet. Just ensure the leaves were plain and not coated in any oils, garlic, or other seasonings. You can offer your dog some fresh water and monitor them as usual, but there's no need for any special action.