Sheikh Muhammad Munajid claimed the mouse is "one of Satan's soldiers" and makes everything it touches impure, The Telegraph reports.
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.
"According to Islamic law, the mouse is a repulsive, corrupting creature. How do you think children view mice today – after Tom and Jerry?
"Even creatures that are repulsive by nature, by logic, and according to Islamic law have become wonderful and are loved by children. Even mice.
"Mickey Mouse has become an awesome character, even though according to Islamic law, Mickey Mouse should be killed in all cases."
Mr Munajid is also the imam who condemned the Beijing Olympics as the "bikini Olympics", claiming that nothing made Satan happier than seeing females athletes dressed in skimpy outfits.
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