"We are working with the school, which is attended by His Royal Highness Prince George, to review its security arrangements after the incident".
The release also noted that while police are part of the security arrangements for Prince George, Thomas's Battersea is responsible for its own on-site security.
In a release, the Metropolitan Police confirmed the arrest of the 40-year-old woman on Wednesday, and said it related to a Tuesday incident at the school "when an individual gained access to its premises".
"Police were alerted and officers attended immediately after the issue came to light".
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". The school has 560 boys and girls aged from four to 13, with around 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.
The young Prince began his education at Thomas's prep school in Battersea, London on Thursday last week.
Kensington Palace said it was "aware of the issue but we would not comment further on security measures".