Sheikh Muhammad Munajid claimed the mouse is "one of Satan's soldiers" and makes everything it touches impure.
But he warned that depictions of the creature in cartoons such as Tom and Jerry, and Disney's Mickey Mouse, had taught children that it was in fact loveable.
The cleric, a former diplomat at the Saudi embassy in Washington DC, said that under Sharia, both household mice and their cartoon counterparts must be killed.
Mr Munajid was asked to give Islam's teaching on mice during a religious affairs programme broadcast on al-Majd TV, an Arab television network.
According to a translation prepared by the Middle East Media Research Institute, an American press monitoring service, he said: "The mouse is one of Satan's soldiers and is steered by him.
"If a mouse falls into a pot of food – if the food is solid, you should chuck out the mouse and the food touching it, and if it is liquid – you should chuck out the whole thing, because the mouse is impure.