The findings come from a study completed by internet comparison service Comparis.
People in French-speaking Switzerland were the most supportive of the plan, with 23.2 percent in favour.
In total, 19.5 percent of Swiss respondents said they would support a compulsory vaccination regime.
Only 15.1 percent of German-speaking Swiss said they were in favour.
Half of those surveyed said the vaccination should be free, voluntary and paid for by health insurance providers.
Almost two thirds (73 percent) supported fines for giving false information at restaurants or clubs, while two thirds (67 percent) said people should be fined for not wearing masks.
Compulsory vaccine for Switzerland?
The likelihood of a compulsory vaccination regime in Switzerland is low, however.
In April, Swiss Health Minister Alain Berset said “Swiss law does not allow us to force someone to get vaccinated against their will”.
As reported by The Local Switzerland in June, a vaccine could be made compulsory in Switzerland for people in certain occupations.
Dominique Sprumont, deputy director of the Institute of Health Law at the University of Neuchâtel, explained that immunisation will be obligatory for people in certain jobs, such as healthcare professionals and others whose work brings them in close contact with the public. But others “can't be compelled by force to vaccinated”, he added.
Sprumont said the vaccine will be compulsory, “but compulsory does not mean forced”.