In a tight race, after two runs just 0.25 seconds separated Walker from event winner Elana Meyers Taylor of the USA, and just 0.11 from claiming the bronze medal.
Rounding out the podium was Meyers Taylor teammate Kallie Humphries in second place with German Laura Nolte in third.
"I'm very happy to start the season off with a top six place," said the 29-year-old Walker.
"Of course we always look for the podium but this is a very different year.
"No-one is messing around and you can see that by how tight the field is but it makes for really fun racing.
Ashley Werner also made her debut in a Monobob World Series event, finishing in 19th place.
Both athletes are aiming to compete for Australia when Monobob makes its debut at the Beijing Olympic Winter Games in February.
Werner and breakwoman Kiara Reddingius also made their World Cup debut in the two-woman bobsleigh event, finishing the highest placed Australians in 19th, with Walker and her breakwoman Sarah Blizzard just behind in 22nd.
The Bobsleigh and Skeleton World Cup tour will remain in Innsbruck for one more week, with additional weekend of competition next weekend..