“Then quickly, like you do in a car, you check under the burqa,” he says.
At one stage, Mr Lieberman is heard telling Mr Gavish that he hears “a lot of nonsense every day” and so will listen to him too.
The minister later tells Mr Gavish to “leave us alone — we have the Israel Defence Forces, the best soldiers in the world” before wishing all soldiers and people in Israel a Happy New Year.
The video mimics the style of Sacha Baron Cohen’s recent satirical series Who Is America, in which he portrays fictional Israeli anti-terrorism expert Erran Morad.
But the clip drew criticism on social media.
Anna Ahronheim, the Jerusalem Post’s military and defence correspondent said it was “Not funny in the least. Especially the segment of taking pictures under the woman’s burqa.”
“The Defence Ministry can do better than this,” she adds.
Orit Sulitzeanu, director of the Association of Rape Crisis Centres in Israel, told the website Mako that “sexual humiliation of Muslim women as a blessing for the New Year is twisted and distorted.”
Sources at the Defence Ministry described the video as a humorous video for the Jewish New Year.