The 35-year-old Dutchman, who currently plays in Qatar for Al-Gharafa, had returned to his hometown of Utrecht when the alleged incident occurred.
Video footage released by Shownieuws shows a man, reported to be Sneijder, dressed in a white T-shirt and sitting on the roof of the car.
According to Algemeen Dagblad, Sneijder has paid compensation following the incident, but the car owners, who wanted to remain anonymous, are not happy.
“Half the neighbourhood was shocked by loud noises,” the car owner told Algemeen Dagblad about the commotion in the street on the night in question. “My husband and I also looked out of our window to see what happened.
“We saw someone on a car, a man, I didn’t recognise him. A lot of police arrived and they even brought a dog. It was not an easy arrest and also not friendly.
“The car is 10 years old, but for us it is very valuable.”
A few days later, reports emerged that Sneijder was allegedly the man arrested for the incident.
The car owner added: “Whether you are a footballer or not, you can’t damage someone else’s stuff. He also p*ssed on it.
“We only knew him from football. We then heard that both he and his management denied that he had done this. That makes us angry now.
“It’s okay to be drunk, but you shouldn’t bother others with that. You keep away from stuff owned by someone else. Couldn’t he have just apologised and bought some flowers?
“It is annoying, but in the more than 50 years that we have lived here I have never experienced anything like this. I hope he learns from it.”
A police spokesperson confirmed that a 35-year-old man had been arrested for the destruction of a car on Balderikstraat in the Zuilen district of Utrecht, but did not want to confirm that the person was Sneijder.