The center-back injured the cruciate ligament in his left knee when Barcelona was training ahead of today's Spanish league match away to Villarreal.
Christensen, 29, will not undergo surgery. Instead, the injury to the anterior cruciate ligament will be allowed to heal on its own.
The center-back played in all six of Denmark's matches in the World Cup qualifiers.
"First of all, I am very sorry for 'AC'. It is also a hard blow for the national team that we cannot use such an important player in the back line," national captain Brian Riemer tells TV 2 Sport.
Denmark will face North Macedonia on March 26. Victory in the semi-final means a final against either Ireland or the Czech Republic a few days later.
The winner of the playoff final will reach the World Cup finals in North America this summer.
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