The 40-year-old, who was not named by police, was arrested after gaining access to the exclusive Thomas's Battersea school on September 12.
She accepted a caution for "causing a nuisance on school property", London's police said in a statement.
A caution is a warning to someone who has admitted an offence. It avoids a court case for both sides but remains on a person's record.
The incident came shortly after George started at the school.
George is third in line to the throne after his grandfather Prince Charles and father Prince William, the Duke of Cambridge.
The police said they were continuing to work with the school on "protective security arrangements" for the young prince.
The future monarch is known as George Cambridge at the £17,600 ($23,000, 19,500-euro) per year school.
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.ng
