Security is being reviewed at Prince George's school after a woman was arrested on suspicion of attempted burglary.
The Metropolitan Police said it was working with Thomas's Battersea in south London following the break-in on Tuesday.
Prince George, four, was not understood to be at the independent school at the time.
The 40-year-old woman remains in custody after being arrested on Wednesday.
A police spokesman 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.
"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."
Prince George only started at the school last week, on September 7.
He was expected to begin by attending school for half-days, before building up to longer hours.
A Kensington Palace spokeswoman said: "We are aware of the issue but we would not comment further on security matters."
Thomas's Battersea educates 560 boys and girls aged from four to 13, with around 20 pupils in each class.
Fees cost £17,604 a year, and increase to £19,884 a year for those in year three and above.