Świątek, the defending champion in Cincinnati, led 4-1 in their women's singles quarterfinal when Rybakina retired with an apparent Achilles injury.
The match lasted just 31 minutes, Polish state news agency PAP reported.
Rybakina appeared to be struggling with her left Achilles tendon and had tape running along the back of her calf.
The world No. 2 requested a medical timeout while serving in the sixth game and returned to the court after consulting with a physiotherapist.
She was unable to serve with full power and decided to retire from the match.
Świątek had beaten Rybakina 6-2, 6-3 in the Canadian Open final in Toronto on August 12, claiming her 26th career title.
Świątek will face third-seeded American Jessica Pegula in Saturday's semifinal. Pegula defeated compatriot Amanda Anisimova 6-4, 2-6, 7-6 earlier on Thursday.
The Pole leads her head-to-head record against Pegula 7-5.
The Cincinnati Open hard-court tournament is the final warm-up for many top players ahead of the US Open Grand Slam, which starts on August 30.
(gs)
Source: IAR/PAP