The now-deleted video was posted on his Instagram story on Tuesday, but is now being widely shared on social media.
Mazepin’s face is not actually seen in the video, which is shot inside of a moving vehicle.
An unidentified hand can then be seen grabbing the chest of a woman in the back seat.
The woman in the video pushes the hand away before putting her middle finger up to the camera.
“The matter is being dealt with internally and no further comment shall be made at this time,” the racing team added.
It was announced last week that the 21-year-old Russian would join Haas F1 team ahead of the new season. The rookie driver has promised to learn from his mistake.
“I have to hold myself to a higher standard as a Formula 1 driver and I acknowledge I have let myself and many people down. I promise I will learn from this.”