BERLIN—Swiss voters narrowly approved on Sunday a proposal to ban face coverings, both the niqabs and burqas worn by a few Muslim women in the country and the ski masks and bandannas used by protesters. The measure will outlaw covering one’s face in public places like restaurants, sports stadiums, public transport or simply walking in the street. It foresees exceptions at religious sites and for security or health reasons, such as face masks people are wearing now to protect against COVID-19, as well as for traditional Carnival celebrations. Authorities have two years to draw up detailed legislation. Two Swiss cantons, or states, Ticino and St. Gallen, already have similar legislation that foresees fines for transgressions. National legislation will put Switzerland in line with countries such as Belgium and France that have already enacted similar measures. The Swiss government had opposed the measure as excessive, arguing that full-face coverings are a …