A mass of boulders weighing around 2,000 cubic metres fell on the road linking the Engadine Valley and Giarsun Ardez.
Clean-up operations continued on Monday to clear the road of the debris, according to cantonal authorities.
A bypass was established for vehicles of less than 3.5 tonnes while heavier vehicles were rerouted through the Ofen Pass.
Two cars were hit by another avalanche in Graubünden on Sunday, but the occupants were able to exit safely from the vehicles, cantonal police reported.
Spring-like conditions have made many snow-covered mountain slopes unstable.
On Friday, an avalanche claimed the life of a 33-year-old forester, who was clearing a driveway with a backhoe beneath the steep northern slope of the Stanserhorn, a mountain in the canton of Nidwalden.
Another slide disrupted the Glacier Express train service in the canton of Valais over the weekend.
Meanwhile, a German tourist in his 60s was seriously injured in Zermatt when a lump of ice weighing 15 kilograms fell on him from a roof, the ATS news service reported.
The man was taken to hospital in Bern for treatment.
Following an unusually cold spell, Switzerland has experienced milder weather over the past few days, with temperatures rising to as high as 23 degrees in Ticino over the weekend.