The 33-year-old is struggling with a recurring Achilles tendon injury.
Karhan will be out of action for three weeks.
“There’s a little tear which means I can’t take part in the tournament,” said Karhan.
“I have a three-week break ahead of me and the World Cup begins in two weeks. So my withdrawal is final.”
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.