The video was quickly deleted, but it was later shared on social media, prompting Haas to release a statement saying the Russian's actions were “abhorrent”.
Mazepin later apologised in a statement of his own, saying he must “hold myself to a higher standard as a Formula 1 driver”.
The woman in the video posted a message to Instagram shortly after the Haas statement was released, saying the incident in the video was “nothing serious at all”.
“I posted this video on his story as an internal joke,” she wrote.
“I am truly sorry. I can give you my word he's a really good person and he would never do anything to hurt me or humiliate me.”
On Thursday, the joint statement by F1 and the FIA explained that Mazepin's actions acted as a reminder of the ethical and diverse values within the series.
“We strongly support the Haas F1 Team in its response to the recent inappropriate actions of its driver, Nikita Mazepin,” the statement reads.
“Mazepin has issued a public apology for his poor conduct and this matter will continue to be dealt with internally by the Haas F1 Team.
“The ethical principles and diverse and inclusive culture of our sport are of the utmost importance to the FIA and Formula 1.”
Mazepin finished fifth in this year's F2 championship, with series champion Mick Schumacher completing the all-new Haas driver line-up in 2021.