Prince George is expected to return to school as normal after a woman was arrested on suspicion of trying to break in.
Security is being reviewed following Tuesday's suspected burglary at Thomas's Battersea, a fee-paying school in south London.
The four-year-old prince, who is currently attending reception classes on a half-day basis, was not understood to be there at the time.
A 40-year-old woman remains in custody after being arrested on Wednesday.
She is reported to have been detained by officers in a square close to the school.
Scotland Yard said it was working with Thomas's Battersea to examine security arrangements following the scare.
It comes less than a week after George's first day at school on September 7.
A police spokesman said: "The arrest at 14:15hrs on Wednesday, 13 September relates to an incident at Thomas's 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."
Along with his classmates, George is currently attending reception during the mornings 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."
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.