Italy, who last failed to qualify for the World Cup in 1958, will play the second leg at home in the most eye-catching of the four ties.
Switzerland, who finished second in their qualifying group despite winning nine of their 10 games, were drawn against Northern Ireland, who last qualified in 1986, with the first match in Belfast.
Croatia, runners-up behind Iceland in their group, will face Greece with the first leg at home. The fourth tie pits Ireland against Denmark, who host the first match.
“We had the toughest qualification group against Netherlands and against France and we played some really good games. If we can play at the level, then we can beat any team in the world, including Italy,” Sweden coach Janne Andersson told Reuters.
“We have a lot of good young players and some experienced players – we have a good mix in the team.
“We have a good mentality in the team, we have confidence.”
His opposite number Gian Piero Ventura did not attend the draw at FIFA headquarters.
Northern Ireland coach Michael O’Neill, whose team includes a number of English second tier players, said his side would make life as difficult as possible for Switzerland, who are bidding to qualify for their fourth successive World Cup.
“We’re here on merit. We were second in our group behind the Germans, of course we can believe we can win it,” he said.
“We can make the tie very difficult for Switzerland. They will be favourites to go through, we believe we are capable of overcoming them.”
Ireland coach Martin O’Neill said: “I know Denmark and I know the manager Age Hareide, he and I used to play together so it will be an interesting confrontation.”
Northern Ireland v Switzerland
Croatia v Greece
Denmark v Ireland
Sweden v Italy
Two-legged ties to be played Nov. 9-11 and Nov. 12-14