The Scandinavian derby is one of four two-legged playoffs to fill the final four places for next year's expanded 24-team tournament in France.
Norway and Hungary get the ball rolling in Oslo on Thursday with Bosnia hosting Ireland in Zenica on Friday. On Saturday, Ukraine host Slovenia in Lviv and Sweden take on the Danes in Stockholm.
The 34-year-old Ibrahimovic, still the Swedes' most potent weapon, was named his country's Footballer of the Year for the 10th time on Monday, fulfilling a promise he made last year to collect the prize again.
"I don't know if I can promise the same thing for next year," said Ibrahimovic, who could play at next year's Olympics as an over-age player.
The playoffs could be the last matches in charge for opposing coaches Erik Hamren and Morten Olsen.
Having missed out on qualifying for the World Cup in Brazil, Sweden's Hamren is unlikely to continue if they go out while Olsen will definitely step down when Denmark's interest ends.
Both teams have seen their midfield ranks depleted by injuries, with the Danes losing Pione Sisto and Leon Andreasen, while Sweden are without Albin Ekdal and Pontus Wernbloom.
Norway failed to automatically qualify when a final-game defeat by Italy allowed Croatia to finish runners-up in Group H but Per-Mathias Hogmo's side will be confident of overcoming a Hungary team who have not reached a major tournament since the 1986 World Cup in Mexico.
The Norwegians have been revitalised by the energetic midfield performances of the likes of Alexander Tettey, Jo Inge Berget and Stefan Johansen, as well as 16-year-old forward Martin Odegaard, and can point to not having lost against Hungary since 1981 as grounds for optimism.
BOSNIA UPBEAT
Bosnia's hopes of reaching the finals have been boosted by the return of top scorer Edin Dzeko who missed their final two group-stage qualifiers with a knee injury.
“Our key players are in good form and this is one of the reasons we are very optimistic,” coach Mehmed Bazdarevic told Bosnian media.
Ireland manager Martin O'Neill has injury and suspension problems to overcome.
Defender John O’Shea and midfielder Jonathan Walters are banned, although both are eligible for the return in Dublin, while striker Shane Long will miss the first leg for further treatment on an ankle injury. Goalkeeper Rob Elliot has also been ruled out with a thigh injury.
Ukraine's clash with Slovenia is a rematch of the Euro 2000 playoff which the Slovenians won 3-2 on aggregate to reach their first major tournament as an independent nation.
Slovenia secured a playoff spot after finishing third behind England and Switzerland in Group E and will look to 36-year old striker Milivoje Novakovic, who bagged six goals in qualifying, to carry the attack to a Ukraine side without injured influential midfielder Ruslan Rotan for both legs.
Ukraine coach Mykhaylo Fomenko also has to fill another gap in midfield with Taras Stepanenko banned for the first leg, along with full back Olexandr Kucher.
(Additional reporting by Zoran Milosavljevic, Philip O'Connor, Zoltan Fazekas and Igor Nitsak; editing by Rob Hodgetts)
