The video, filmed by a group of friends calling themselves Collective Bièvre, shows four white sheep chasing after a black sheep, mimicking the SVP's controversial poster which shows a white sheep kicking a black sheep out of Switzerland.
However in the light-hearted video, when the white sheep catch up to the black, they embrace her in a group hug – and are quickly joined by several passers-by.
The video ends with the slogan: “Don't be a sheep. You are not racist”.
Since the group published their video on Facebook it has been viewed 667,000 times, has over 11,000 shares and hundreds of comments, mostly positive.
Speaking to radio station Rouge FM, group member Natalie said she and her friends felt uncomfortable at the image of Switzerland portrayed by the SVP in its poster, and so decided to use the party's own imagery to lambast its message.
“For us, it's not a question of left or right, it's a question of humanity and equality for everyone under Swiss law,” she said.
The SVP's initiative, which will be voted on by the public this Sunday, “gives an image of Switzerland as intolerant and closed,” she added. “We hope that those who saw the video will be happy to see a more positive image.”
Opponents of the proposal say that if it is passed, up to 18,000 foreigners could be expelled from Switzerland every year for what could be relatively minor offences.
The initiative goes further than a similar one, approved by the electorate in 2010, that requires the expulsion of foreigners convicted of serious crimes such as murder, rape, armed robbery or drug trafficking, as well as abuse of social benefits.
Not everyone has reacted well to the video, however.
One commenter, Marine Rohrer, said: “Where is the racism in this initiative? It's not rejecting foreigners, but foreign criminals. There's some nuance there, no?”