Fortunately, no-one was injured as a result of the falling rock, cantonal police said on Monday.
But the boulder, about four metres in size, caused around 10,000 francs’ worth of damage when it crashed through two barriers and a wildlife fence on Sunday night, police said.
The rock landed in the emergency lane in an area of the highway that passes through rough mountain terrain, where the lanes are not separated.
The A13 links the canton of Saint Gallen in northeastern Switzerland with the canton of Ticino to the south, passing through Graubünden, and offering a route to Italy.
But while the northern section of the road is a motorway with a 120 kilometres an hour speed limit, other sections are classified as an expressway with speed limits from 80 to 100 km/h.
The rock ended up in a stretch of the A13 near the Wegerhaus tunnel, south of Chur, police said.
The road office is looking into whether new safety measures may be necessary to prevent future such rockfalls.