The Polish world No. 2 fell 6-3, 1-6, 0-6 to the Moscow-born Kazakh at the eight-player event in Saudi Arabia on Monday.
Świątek opened her WTA Finals campaign with a 6-1, 6-2 victory over American Madison Keys.
She will now take on Amanda Anisimova of the United States in her last group-stage match on Wednesday.
The 2025 WTA Finals event began on November 1 and runs until Saturday.
Świątek won the 2023 WTA Finals but suffered an early exit in Riyadh last year.
(gs)
Source: IAR, PAP, polskieradio24.pl