After finishing second in their qualification groups, the two nations must square off in a two-legged tie to qualify for next year's tournament in Russia.
Switzerland are regarded as marginal favourites having won all but one of their 10 qualifying matches, and Shaqiri is confident that his nation have enough quality in their ranks to get the better of Michael O'Neill's men.
The 26-year-old is quoted by The Mirror as saying: "The most important thing is to qualify for the World Cup and I am confident that if we play good, we will do that. We are going to Northern Ireland first, and will try to take something back for when we play at home.
"They will be two tough games — they were in a tough qualifying group with Germany and the Czech Republic — but we have the quality and I think we are the better team.
"To go to the World Cup would be great and I am confident we are going to go through."
The first leg takes place at Lansdowne Road on Thursday night.