Trump's executive order, signed last Friday, has provoked widespread condemnation around the world, including in Britain, where 1.7 million people have so far signed a petition against Trump's proposed state visit to the UK.
The issue will now have to be debated in the UK parliament on February 20th.
On Monday independent Swiss mobilization site campax.org started its own petition which, as of Wednesday morning, had 7,249 signatures.
“The selective exclusion of foreigners from predominantly Islamic countries by the Trump government is an unacceptable act against human dignity and religious freedom,” says the petition's text.
Signatories call on the Swiss government “to take a stand” and tell President Trump he is “persona non grata and therefore not welcome in Switzerland until further notice”, it reads.
Speaking to 20 Minuten, Campax president Andreas Freimuller said “Trump's policies could have serious consequences for many people around the world” and that the Swiss government should not be shy in telling the US president he is not welcome here.
However the petition has not been well received by many politicians.
“Switzerland should speak to every government of the world, even if bad people are in power. And even if we don't accept Trump's policies we should seek dialogue with him,” Swiss Socialist Party MP Tim Guldimann told the paper.
Whilst acknowledging that people have a right to protest, Green MP Sibel Arslan said that “advocating a ban in response to a ban does not benefit Muslim countries or Switzerland or the US”.
It would be better to criticize the US President's policy and try to reason with him, Arslan added.
Other MPs told the paper that Switzerland should stay neutral and that it would be a diplomatic faux pas to put Trump on a black list.
There has been no official reaction to the petition from the Swiss government.
However earlier this week Swiss foreign minister Didier Burkhalter criticized Trump's executive order, saying it “goes in the wrong direction”.
On January 21st, the day after Trump's inauguration, more than 2,000 people gathered for the Women's March in Geneva, part of a global movement in support of civil rights.