The boat, carrying the instructor and a 32-year-old student, keeled over before 3pm on the Lake Uri finger of the lake in central Switzerland, Uri cantonal police said.
A nearby worker noticed the men in the water and attempted to rescue them.
Efforts to resuscitate the instructor failed.
He died in the port at Flüelen, the SDA news agency reported.
The injured student was transported to hospital by ambulance, police said.
The exact circumstances of the accident are the subject of ongoing investigations.
But a police spokesman told SDA that at the time strong winds were blowing and that there were white caps on the lake.
The incident occurred in the eastern part of the lake that straddles four cantons.