Sixth seed Tsitsipas was trailing the opening set 2-1 when he was forced to quit the Green Group match, handing Finals debutant Rune his first ever win in the season-ending tournament.
“My apologies to all the fans and the crowd who came to support me today. Really I’m gutted that I wasn’t able to finish the match,” Tsitsipas, 25, told reporters.
“My doctors and the countless visits that I had in the last few days suggested that I play… Unfortunately I felt terrible on the court. I did what I could do in best possible way to be ready and fit for this match, But it didn’t work out for me.”
Hubert Hurkacz will now step in to play Tsitsipas’ final match against Novak Djokovic with no chance of progressing to the semi-finals following two defeats for the Greek.
Tsitsipas said after pulling out that he had felt problems during his warm up and that once on the court he felt too much pain to complete the match.
“The pain was very big,” he added.
“I’ve gone through pain during matches in the past… But this was clearly too much to handle and I had to take the difficult decision to do what I did.”
He had insisted that there was nothing wrong with him physically after Sunday’s straight-sets defeat to Jannik Sinner, playing down reports of an elbow injury which curtailed practice ahead of his tournament opener.
However Tsitsipas hinted that a lack of rest in a packed schedule could have contributed to him having to drop out.
The ATP has come under fire from players and coaches for scheduling which often leads to late-night matches and short recovery times during tournaments.
“I do believe that it’s maybe a combination of a lack of rest and not that good a preparation,” he said.
Later Djokovic will attempt to reach the semi-finals with a match to spare when he takes on home hope Sinner, who is aiming to become the first ever Italian to reach the tournament’s last four.
Djokovic secured top spot in the year-end world rankings for a record-extending eighth time with his opening win over Rune on Sunday and will qualify if he beats Sinner.
This year the 36-year-old has won three Grand Slams to take his total to an all-time best 24, as he bids for a seventh Finals title.
Victory in Turin would make him the record winner in the singles, one ahead of old foe and retired great Roger Federer.
Sinner meanwhile will make the semis if he beats Djokovic in two sets, a tall feat as he has lost all three of his previous encounters with the Serb.