His club Hanover 96 said on their website (www.hannover96.de) that the 32-year-old had sliced open his left hand with a sharp knife while opening a large package at home.
An operation to repair damage to a tendon was carried out on Saturday, leaving Andreasen, who won the last of his 20 caps in a friendly against Turkey in 2014, with his hand and forearm in a protective cast, the club added.
"It's unfortunate for him and bad for the team," Denmark coach Morten Olsen said in the DBU statement.
Denmark face Sweden in Solna on Nov. 14 before hosting the return leg in Copenhagen three days later.
(Reporting by Philip O'Connor; editing by Toby Davis)
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