Police spokeswoman Cindy Beer told SRF television that police were alerted at 10.39 a.m. Monday (0839 GMT) to the incident. She said "we can't say exactly what happened at this point."
"We just know that a person wounded several people," Beer said, AP reported.
The man's whereabouts are unknown and the old town in Schaffhausen is currently sealed off, Beer said, adding that police can't say with certainty what implement the man used to wound the others.
A rescue helicopter was being used to aid the victims.
Schaffhausen is a city of about 36,000 north of Zurich near the border with Germany.
Police and prosecutors refused to elaborate further as the manhunt was ongoing.