There had been speculation that Federer was struggling with the problem and that only increased when he failed to show up for a scheduled practice session on Sunday afternoon.
The announcement was made following the doubles final, with Federer taking to the court to explain the situation to the fans.
He said: "Unfortunately I'm not match fit to play match tonight. Clearly I wish it wasn't this way. You try all year to be ready for the ATP World Tour Finals and I didn't want to end this way.
"I tried everything I could last night and today - painkillers, rest - until the very end, but I can't compete at this level with Novak. In a final like this and at my age, it would be too risky. I hope you understand."
Federer had earlier battled for almost three hours to defeat countryman Stan Wawrinka, saving four match points, and he is unlikely to recover in time for Switzerland's Davis Cup tie against France next week.
Organisers announced that British No 1 Andy Murray will instead face Djokovic in one pro set, and then join John McEnroe in a doubles match against Tim Henman and Pat Cash.
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