The suspect, an unidentified man who remained at large, fired several shots in two different locations in Sion, a town of about 35,000 people in the southwest of Switzerland, Reuters reported.
Police said the attacker's motives were unknown.
"According to initial findings, the perpetrator knew his victims," police said.
Switzerland, a country of around 9 million, has a high rate of gun ownership.
Small Arms Survey, a Swiss-based organization that monitors global trends in armed violence, estimates the number of firearms in civilian possession at 2.3 million.