The graffiti was critical of President Donald Trump and Elon Musk. ABC7 has blurred part of it, due to profanity.
The vandalism was discovered Friday at the newly-constructed dealership on Dundee Road in Buffalo Grove.
The woman is facing criminal damage to property and trespassing charges, police said. Authorities did not provide the name of the suspect.
ABC7 reached to the dealership for comment, but has not heard back.
Vandals have been targeting Tesla dealerships across the country.