The woman in the clip moves Mazepin's hand before raising a middle finger and swatting the camera away.
Haas issued a scathing statement on Wednesday where it said they would be taking internal action over the incoming driver's antics.
"Haas F1 Team does not condone the behaviour of Nikita Mazepin in the video recently posted on his social media," the statement reads.
"Additionally, the very fact the video was posted on social media is also abhorrent to Haas F1 Team.
"The matter is being dealt with internally and no further comment shall be made at this time."
Mazepin, 21, was quick to follow from the team statement with one of his own, where he apologised for his actions.
"I would like to apologise for my recent actions both in terms of my own inappropriate behaviour and the fact that it was posted onto social media," Mazepin said.
"I am sorry for the offence I have rightly caused and to the embarrassment, I have brought to Haas F1 Team.
"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."
A week after being named as joining the Haas team for the 2021 season, Mazepin finished the 2020 F2 season in fifth place.
Mazepin will partner alongside Mick Schumacher in the new look Haas outfit for next season, but his on track antics in the final race of the season raised the eyebrows of team principal Guenther Steiner.
"I've seen the F2 race, he got the penalty," Steiner told RaceFans.net.
"I think it's part of learning and for sure we have got our work cut out, I guess, I think I'm right there.
"We need to learn from this and see that these mistakes are not done."
The final race of the Formula 1 season will take place in Abu Dhabi.