What is the ruling on unintentionally killing animals—such as a sheep, a cat, or a bird—by running them over with a car?

It is not permissible to intentionally kill living beings unless an exception is made by Sharia. There is no sin upon one who kills an animal by mistake, for Allah Almighty says: "And there is no blame upon you for that in which you have erred, but [there is blame for] what your hearts intended." The killer is obligated to pay the value of the animal to its owner. If it is not owned by anyone, then he must seek forgiveness, and it is preferable for him to give charity.