The accident occurred around 8.20am as the man was driving his rig toward Seewen in the central part of Switzerland, Schwyz cantonal police said in a news release.
The truck hit a patch of ice and broke through railing of the bridge, tumbling 10 metres into the icy river with the driver inside the cab, the release said.
The driver was able to extricate himself from the vehicle and was taken to hospital for treatment of minor injuries, police said.
Firefighters put a boom in the water to contain fuel spilled from the truck.
Later in the day, a mobile crane hoisted the truck out of the river, which flows into Lake Lucerne in Brunnen.
Police are looking for witnesses who may be able to cast further light on the circumstances of the accident.
Icy conditions in Schwyz were also blamed for a head-on collision of two vehicles in Ibach, near Brunnen, on Tuesday.
Police said a 27-year-old driver lost control of his car and slammed into an oncoming vehicle driven by a 54-year-old man who was taken to hospital for “moderate” injuries.
Both vehicles were write-offs.