The 33-year-old man must pay the sum to the Danish Football Association (DBU), the High Court in Copenhagen ruled on Tuesday.
The fan had appealed against a 2009 decision by the Copenhagen City Court which had ordered him to pay the DBU 900,000 crowns, but the High Court doubled the amount.
"The person in question's acts represent the biggest attack on Danish football's integrity," Jim Stjerne Hansen, secretary-general of the DBU, said in a statement.
"His violent assault on the referee cost us an almost spotless reputation within the football world and 2.2 million crowns," Hansen said.
The match on June 2 2007, at the Parken Stadium in Copenhagen was abandoned in the final minutes when the fan rushed on to the field and tried to hit German referee Herbert Fandel who had just sent off Denmark's Christian Poulsen and awarded the guests a penalty with the score at 3-3.
UEFA later awarded Sweden a 3-0 victory, and the loss to Sweden meant that Denmark failed to qualify for Euro 2008.
The DBU had sought 2.2 million crowns in damages after it was fined by UEFA and Denmark were banned from playing their next two qualifiers at Parken.
The court's award was lower than the DBU's claim because the court deemed the number of spectators who would have attended a match against Lichtenstein to be lower than the DBU's estimate.
The DBU said it was willing to discuss reducing the fine with the fan, whose name has not been released by officials. He has said he would be bankrupt if he had to pay.
Danish football fans have created groups on social network Facebook to raise funds to help the fan pay the damages. Poulsen has also said he would be willing to contribute financially 'as it was basically my fault'.
In 2007, the fan was convicted of attempted assault and trespassing and given a suspended 30-day jail sentence, which was reduced to 20 days on appeal.
The fan admitted he was drunk and entered the pitch illegally, but rejected the violence charge.
