The woman is being held at a south London police station following her arrest for breaking into the school.
A Met spokesperson said officers had "attended immediately after the issue came to light".
The police said Thomas's Battersea is responsible for building its own security but pledged to continue to "work closely" with the school.
George had his first day at the school only last week.
The four-year-old prince started at the £18,000-a-year preparatory school on 7 September.
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A spokeswoman for Kensington Palace told CNN it was "aware of the incident" but wouldn't comment on security matters.
Security at the school will now assessed following the incident yesterday.
As Prince George begins academic life at his new school, Thomas's Battersea, a royal source told PEOPLE that his parents, Prince William and Princess Kate remain committed to dropping George off and picking him up from school.
Headmaster Ben Thomas released a statement in March about Prince George joining the school.
The school accommodates boys and girls between four and 13; prospective two and three-year-olds are called in for an assessment to determine their suitability, although the test relies on natural intelligence rather than academia. The approximately $23,000-per-year school teaches a range of traditional subjects, along with ballet, art, drama, French, music and physical education.
The guide, which said 19 languages are spoken in the homes of pupils, added: 'The school celebrates and appears to make the most of this range of different cultures'.