World number six Monfils, a debutant at the tournament after an impressive year in which he reached the U.S. Open semi-final, could not make the last four in London after losses to Milos Raonic and Dominic Thiem in his opening two matches.
"Definitely I can't play for tomorrow because I feel worse and worse with my ribs," he told reporters.
"I couldn't practise."
Monfils sustained the injury in Stockholm in October and was told that it would be a six-week recovery period.
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"I tried to make it, but I couldn't," he said.
Defending champion Djokovic has already booked a semi-final spot but will be desperate to beat Belgium's Goffin to grab another 200 points in the race to beat Andy Murray to the end-of-year world number one ranking.
Goffin finished the year ranked 11th.
(Reporting by Martyn Herman; Editing by Toby Davis)
