The music mogul - who is engaged to make-up artist Mezhgan Hussainy - discovered the baby animal hiding in his `American Idol` dressing room and took the creature home where he tenderly cared for it.
A source told the National Enquirer magazine: "Simon actually took the mouse home to his mansion in Los Angeles. He then stayed up half the night feeding it milk. Simon became so attached to his new little pet he even took it on trips."
The music mogul is known for his love of animals but has previously claimed his lifestyle is too hectic to give a pet the care and attention it needs.
He has said: "When I was growing up, we had pets, and I was taught early on that you have to respect animals. I don`t have pets now, simply because I travel too much to take on the responsibility. But owning pets has had an immensely positive impact on my life and I think animals deserve our protection."
The multi-millionaire star has previously given money to several animal charities, secretly donating $165,000-a-year to an animal shelter run by `Exorcist` actress Linda Blair in California.
He also donated most of the 179 mirrors he received for his 50th birthday last year to be auctioned to raise money for the Battersea Dogs Home in London.