The British number one's withdrawal from next week's event in Moscow means France's Caroline Garcia now takes the final berth in the field for the WTA Finals in Singapore the following week.
Garcia is 11/2 with Sky Bet to win the prestigious tournament having stormed through the Asian swing with WTA titles in Wuhan and Beijing.
However, Konta is hoping to recover in time to take an alternate place, which would see her claim the spot of any player forced to pull out.
If she does not make it in Singapore, she hopes to be fit to compete in the WTA Elite Trophy in Zhuhai - a tournament for the best players of the year who did not qualify for the WTA Finals.
Konta said: "As you all might have seen, I've needed to withdraw from Moscow.
"I am obviously sad that I couldn't continue my battle to make it to Singapore, however it's a massive congratulations to all the girls that have qualified.
"I am working hard to recover well and still make it to Singapore as an alternate and to be competing in Zhuhai.
"Thank you everyone for the continued support and I'll be seeing you guys soon on court."
It is the second year in a row that the 26-year-old has narrowly missed out on reaching the WTA Finals.
Twelve months ago, she travelled to Singapore and took part in all the pre-tournament publicity only for Svetlana Kuznetsova to usurp her at the final moment by winning the Kremlin Cup.
New world number one Simona Halep is the 4/1 favourite for the WTA Finals, which take place from October 22-29.
Wimbledon champion Gabrine Muguruza, Karolina Pliskova and Elina Svitolina are co-second favourites at 5/1.
Caroline Wozniacki (13/2), Venus Williams (8/1) and French Open winner Jelena Ostapenko (8/1) complete the eight-woman field.
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