As he continues his comeback from ankle and groin surgery, Rutherford has decided to miss the global event to regain full fitness ahead of the European Championships in Berlin in August.
"My performance from the British championships to the Indoor Grand Prix in Glasgow at the weekend showed improvement but it was still not at the level I demand of myself," the 31-year-old said in a statement.
"It has not been an easy decision but I have therefore chosen to withdraw from the world indoor championships.
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"I am committed to becoming the first long jumper to win three European titles in a row and will be training hard over the coming months to return to the track as fit as ever."
Rutherford's withdrawal leaves the size of the British and Northern Irish team at 31 ahead of the championships, which starts on Friday.
"Greg is a great role model and ambassador for the sport as demonstrated at the British Indoor Championships and Indoor Grand Prix in Glasgow and we look forward to seeing him back fully fit in the summer," British Athletics performance director Neil Black said.
(Reporting by Hardik Vyas in Bengaluru; Editing by Mark Potter)
