He picked it up on his first day back in full training following a separate knee injury, a week before the month-long tournament kicks off on Friday.
The 23-year-old joins Ghana's Michael Essien (knee injury) and very probably the Ivory Coast captain Didier Drogba (broken bone near elbow) on the sidelines, leaving the finals likely to miss three of its biggest African names.
Obi Mikel learned on Saturday that he would miss this month's showpiece (June 11-July 11) after a scan showed he would not recover in time.
Nigerian Football Federation (NFF) spokesman Idah Peterside said Nigeria's key midfielder had pulled up after some 50 minutes of training in Richards Bay on Friday with severe pain.
"He had been complaining about a niggle in the ankle when we first arrived in South Africa but after training yesterday it really flared up. His knee was doing fine and you can understand he is devastated about this new problem.
"He is not sure how it happened. It wasn't a tackle with another player or anything like that," Peterside said.
"It was been very emotional for him and for the other players too. The team has been trying to consol him. He's been to the Olympics but this was to be his first World Cup."
Obi Mikel will return to London for further medical examinations at the weekend, the spokesman added.
Nigeria's team were flying on Saturday from their coastal base camp to Johannesburg, where they play a friendly against North Korea on Sunday.
Obi Mikel, who has scored twice in 30 appearances for his country, is being replaced by the uncapped Brown Ideye, a striker from French club Sochaux, the NFF said.
On Friday, England's captain Rio Ferdinand also joined a lengthening casualty list with a knee ligaments injury which rules him out of the tournament too.
