Monfils had lost both his group stage matches at London's O2 Arena and no chance of making the semi-finals.
Monfils had lost both his group stage matches at London's O2 Arena and, with no chance of making the semi-finals, the Frenchman decided not to risk aggravating the problem in his final match, which was due to be against Novak Djokovic on Thursday.
"Definitely I can't play tomorrow because my ribs feel worse and worse," Monfils said.
"Even yesterday was tough in the game. I couldn't practise."
Monfils originally suffered the injury in a match in Stockholm last month and had been troubled by it during his defeats against Dominic Thiem and Milos Raonic in London.
"You work so hard for this moment and not to be able to finish is a huge disappointment," he added.
Belgium's David Goffin will step in to replace Monfils against Djokovic who is chasing a fifth straight Tour Finals crown to equal Roger Federer's record of six titles.