Meyer clocked 9 minutes, 39 seconds before later starters faced head winds on the 8.1-kilometre (5-mile) time trial route around Quinto.
The six-time world champion on the track was 10 seconds faster than Niki Terpstra of the Netherlands. Third-place Heinrich Haussler trailed his fellow Australian by 14 seconds.
“Obviously I had some help with the weather,” said Meyer, who is now focusing on being a full-time road rider. “The wind was very favourable for me being one of the first riders off. … To get the (yellow) jersey in a World Tour race, I can’t believe it at the moment.”
Cancellara, the former Olympic and four-time world champion in time trial, trailed by 22 seconds.
The second stage on Sunday has been diverted from the steep Nufenen pass at 2,478 metres (8,130 feet) altitude because of snow blocking the intended route.
The shortened stage now starts in Ulrichen and finishes at the ski resort of Crans-Montana.