The other ties decided at the Home of FIFA in Zurich will see Greece host Romania in the first leg while Iceland will play Croatia at home before the away trip in the second leg.
The play-off draw is:
Portugal (ranked 14) v Sweden (25)
Ukraine (20) v France (21)
Greece (15) v Romania (29)
Iceland (46) v Croatia (18)
The first leg of the play-offs will be played on Friday 15 November (Saturday 16 November) with the second legs four days later.
The play-offs mean one of football's superstars is certain to miss out on the World Cup next year after Cristiano Ronaldo's Portugal was drawn against Zlatan Ibrahimovic's Sweden.
France will face a tough battle against Ukraine, which England could not beat in two qualifying matches.
Portugal will go into the play-offs as favourite with stars such as Real Madrid's Ronaldo, Manchester United's Nani and Monaco playmaker Joao Moutinho, but Paulo Bento struggled in what had looked a straightforward qualifying group, finishing runner-up to Russia.
Sweden is more than capable of causing a surprise, especially with Paris Saint-Germain forward Ibrahimovic leading from the front.
Greece will fancy its chances to pregress against unseeded Romania while Iceland could not have asked for better in its attempt to qualify for a first ever World Cup after being drawn against Croatia, perhaps the least dangerous of the four seeded nations on recent form.