Antonsson suffered the injury playing for club side FC Copenhagen in their derby with Brondby.
"The x-ray on Monday morning showed a little break in a bone in the hand. I'll go to Malmo on Tuesday to try out a special protector - with that, I should be able to train as normal and be available to play," Antonsson told the Swedish FA's website.
Sweden coach Erik Hamren is already missing first-choice centre backs Olof Mellberg (suspended) and Daniel Majstorovic (injured),
Sweden, who failed to qualify for the 2010 World Cup in South Africa, are third in Group E on six points, behind the Netherlands (12) and Hungary (9), with the Swedes having a game less played.
Goalkeepers: Andreas Isaksson (PSV Eindhoven), Johan Wiland (FC Copenhagen)
Defenders: Mikael Almeback (Orebro SK), Mikael Antonsson (FC Copenhagen), Andreas Granqvist (Groningen), Mikael Lustig (Rosenborg), Oscar Wendt (FC Copenhagen), Jonas Olsson (West Bromwich Albion)
Midfielders: Emir Bajrami (FC Twente), Rasmus Elm (AZ Alkmaar), Pontus Wernbloom (AZ Alkmaar), Martin Olsson (Blackburn Rovers), Kim Kallstrom (Olympique Lyon), Christian Wilhelmsson (Al Hilal), Sebastian Larsson (Birmingham City)
Forwards: Johan Elmander (Bolton Wanderers), Alexander Gerndt (Helsingborgs IF), Marcus Berg (PSV Eindhoven), Markus Rosenberg (Racing Santander), Zlatan Ibrahimovic (AC Milan)
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