The arrested woman was taken to a south London police station, where she was being held in custody.
The Metropolitan police said: “We are working with the school, which is attended by His Royal Highness Prince George, to review its security arrangements after the incident. Police were alerted and officers attended immediately after the issue came to light.
“Police are part of the protective security arrangements for the prince and we will continue to work closely with the school, which is responsible for building security on its site.”
George, aged four, started in the reception class last week. The school has 560 boys and girls aged four to 13, with about 20 pupils in each class. Fees are £17,604 a year, and increase to £19,884 a year for those in year three and above.
George was at school on Tuesday but it is unlikely he would still have been there when the incident happened. Last week the school said new pupils were starting on half-days and building up to staying for lunch.
A Kensington Palace spokeswoman said: “We are aware of the issue but we would not comment further on security matters.”