The X Factor judge is said to have discovered Leanne Zaloumis in his house on Saturday night, coming face-to-face with her when he investigated an upstairs noise.
Zaloumis, who was allegedly armed with a broken brick, was charged with aggravated burglary, and appeared at West London Magistrates' Court this morning.
Cowell's publicist Max Clifford said: "It was very frightening for Simon who told me it was like something from a horror movie."
Speaking on This Morning, Clifford said that Cowell had been at home watching an interview with himself and fellow Britain's Got Talent judge David Walliams on Jonathan Ross's chatshow when the incident took place.
"His housekeeper was there and his security was close by so she was quickly apprehended," he added. "It was terrifying, but as Simon said, 'You've got to say I was lucky, it could have been a gun or a knife'."
Zaloumis, who only spoke to confirm her name and south-east London address, will next appear in court on June 12 when the case will be heard by a Crown Court judge.
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Watch Cowell discuss the new series of Britain's Got Talent with Digital Spy below: