Osaka's victory on Thursday guaranteed that she will stay No. 1 in French opening.
"I didn't feel anything yesterday. That's why I'm a little confused right now because I literally woke up in the morning and couldn't move my thumb," Osaka said. "So I was like," Maybe I slept on it, and maybe it will go away. "But it didn't."
Bertens, who won the Madrid Open last week, will meet Johanna Konta for a place in the final.
Tsitsipa's semifinal opponent will be Rafael Nadal, who beat Fernando Verdasco, 6-4, 6-0, on Friday.
Nadal has admitted only six games in six sets at Foro Italico. But he has fallen into the semi-finals in his last three tournaments – all on his favorite clay. One of these losses was that of Tsitsipas, in Madrid last week.
Also the last four were Diego Schwartzman, who beat Kei Nishikori for the first time in four attempts, 6-4, 6-2, to reach his first Masters Series semifinals.
The 24th ranked Schwartzman faces top-ranked Novak Djokovic or his fellow Argentine Juan Martín del Potro.
On the women's side, Karolina Pliskova passed Victoria Azarenka, 6-7 (5), 6-2, 6-2, and faced one of two qualifiers, Kristina Mladenovic or Maria Sakkari, to a place in the final.
Osaka also pulled a semifinal in Stuttgart, Germany last month, due to a stomach injury. And she retired from her previous meeting with Bertens in last year's WTA finals with a leg injury.
"I feel that abbot could have been helped, but I don't think I could have helped it because I didn't know what caused it," Osaka said. "I don't know why I have it."