Scotland Yard said a 40-year-old woman has been arrested over an incident at Thomas’s Battersea.
A review of security arrangements has been launched following the arrest.
The young prince started at his new school last week.
A spokesman for the Metropolitan Police said: “The arrest at 14:15hrs on Wednesday, 13 September relates to an incident at Thomas’ Battersea School on Tuesday, 12 September when an individual gained access to its premises.
“The arrested woman was taken to a south London police station where she remains in custody.
“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.”
He added: “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.”
A Kensington Palace spokeswoman said: “We are aware of the issue but we would not comment further on security matters.”