The world number one and two were due to renew their rivalry at London's O2 Arena on Sunday.
However, Federer's epic semi-final battle with Stanislas Wawrinka - which saw the former save four match points before eventually seeing off his Davis Cup team-mate - took its toll on the 33-year-old's body.
Second seed Federer took to the court ahead of the scheduled 6pm start and revealed he was unable to compete due to a back injury.
"I hope you understand I wanted to come out personally and excuse myself for not playing," an apologetic Federer told the crowd.
"I'm sorry I'm not fit to play the match.
"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."
It remains unclear whether Federer will be able to represent Switzerland in next weekend's Davis Cup final against France in Lille.
Djokovic, meanwhile, ends a successful 2014 as only the third man to have won the season-ending event three years in succession.
However, the Serbian admitted the manner of his triumph meant he would not celebrate too much, before going on to wish Federer a speedy recovery.
"At this moment it is hard to talk about this trophy," said Djokovic. "I don't celebrate winning like this.
"I feel really sorry for Roger for not being able to come out on the court, he is one of the biggest competitors and always gives 100 per cent.
"I am sure if he could have come out he would have. I wish him all the best for his recovery, he has an important week ahead of him with the Davis Cup final."