Insulin can affect pets differently, so it is difficult to say whether or not it will make your pet sleepy. Generally, however, insulin is used to regulate blood sugar levels and can cause drowsiness in some animals. If your pet has diabetes, it may require insulin injections to help manage its condition. If this is the case, you may notice that your pet becomes more lethargic after an injection. It is essential to consult with a veterinarian if you have any concerns about the effects of insulin on your pet. Your vet can guide dosage and any potential side effects that may occur.