Sweden will host Serbia in Stockholm, while Ukraine take on Turkey in Ingolstadt, Germany, less than a week before they clash at the European Championships in Kiev.
Ukraine and Sweden will meet in Group D at Euro alongside England and France.
Sweden accounted for Iceland 3-2 last week with AC Milan striker Zlatan Ibrahimovic scoring and setting up another in Gothenburg.
Ibrahimovic is again likely to shoulder much of the load up front against Serbia, while Galatasaray forward Johan Elmander could feature in his return from injury.
Elmander was included in Sweden’s final squad for Euro despite having a fractured metatarsal bone in his right foot.
Sweden and Serbia have faced off only once before, with the Serbians prevailing 2-0 in Belgrade three years ago.
Ukraine tackle Turkey on the back of recent hit outs against Estonia and Austria.
Oleg Blokhin’s men accounted for Estonia 4-0 before suffering a 3-2 loss to Austria on Saturday.
Ukraine twice drew level through midfielder Oleg Husyev before Austria’s Marko Arnautovic struck the winner in the 89th minute.
The defeat was Ukraine’s first in seven matches – a streak dating back to last September.
Elsewhere, France will aim to extend their undefeated run to 21 games on Tuesday when they host Estonia in Le Mans.
Laurent Blanc’s side have won 14 of their last 20 matches, overcoming the likes of England, Brazil and Germany in the process.
In other fixtures not involving Euro-bound countries, Belarus host Azerbaijan, Kazakhstan travel to Armenia and Austria take on Romania in Innsbruck.
Philippines and Indonesia will face off in Manila.
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