This injury comes nine days before the start of the year-end Masters in Turin (November 13-20), which brings together the eight best players of the season.
The Spaniard, who became the youngest world No.1 in history at 19 after his coronation at the US Open in September, was cautious but not alarmist about his chances of participating.
"I will go home, take exams to know the importance of the problem, and from there we will see with my team the work and the time that I will have to try to go to Turin at 100%" , he replied at a press conference.
Massed at the change of sides at 6 games to 5 in his favor in the second set, under the ribs, left side, Alcaraz said stop at 3 points to 1 in favor of Rune in the decisive game.
"I felt something in the abdominals in the second set. At the end, it got worse, I preferred to give up," he explained.
"It limited me in a lot of things, to hit my forehand, on serve, when I turned, it hurt quite a bit," described "Carlitos".
"Maybe if I had continued I should have stopped for something much more serious, I preferred to stop before it got worse," he added.
- 16th victory in a row -
Before that, Alcaraz had experienced two first express rounds in the Parisian hall.
Rafael Nadal beaten at Bercy, the young Spaniard even had the opportunity to make sure to end the year on the throne of world tennis in the event of a title on Sunday.
After his retirement, he left the French capital with a thousand points ahead of Nadal. A faultless run in Turin will earn 1500.
Alcaraz exploded to the highest level in 2022 by winning its first Grand Slam trophy and its first two in Masters 1000, in Miami and Madrid. But since his title in New York in mid-September, his best result remains a semi-final in Basel last week.
The first semi-final in Paris will oppose Rune to Félix Auger-Aliassime.
In search of a fourth trophy in as many weeks, after Florence, Antwerp and Basel, the 22-year-old Quebecer has chained a sixteenth victory in a row at the expense of the American Frances Tiafoe (21st), dominated 6-1, 6 -4.
Four titles in as many weeks: such a performance has not been achieved for more than forty years. In the fall of 1981, Ivan Lendl had even won five in five weeks.
World number 8 and qualified for the first time for the Masters, "FAA" invites itself to the last four in the Masters 1000 for the second time in its career (after Miami in 2019).
The last two quarter-finals oppose in the evening (from 7:30 p.m.) Novak Djokovic to the young Italian Lorenzo Musetti (23rd), and the world No.5 Stefanos Tsitsipas to the unexpected American Tommy Paul (31st).