London’s Metropolitan Police said the woman was arrested after someone gained access to the school in west London on Tuesday.
As the BBC reports, police said they are "working with the school... to review its security arrangements".
While police have not provided details about what happened, the woman is believed to have allegedly gained access to the school. She remains in custody.
A Kensington Palace spokeswoman said they were aware of the alleged security threat.
“We are aware of this issue but won't comment on security matters,” she said, the ABC reports.
Four-year-old Prince George stared school last week at the prestigious private school, and was photographed arriving at the gate with his father, Prince William.