The American world number two, 35, has not played since reaching the semi-finals of the US Open in September.

Williams' place could go to British number one Johanna Konta, who is ninth in the rankings, although she has an abdominal injury.

The top eight players qualify automatically for the end-of-season finals, which run from 23-30 October.

Konta, who reached the final of the China Open this month, pulled out of last week's Hong Kong Open and will not compete in this week's Kremlin Cup.

She will be overtaken in the rankings if Spain's Carla Suarez Navarro or Russian Svetlana Kuznetsova, 10th and 11th in the rankings respectively, win the tournament in Moscow.

Konta, 25, is aiming to become the first British female player since Virginia Wade in 1980 to reach the finals.

Williams, who has won five Tour Finals, said: "I am really, really bombed that I won't be able to compete.

"It has been a really tough year for me, just dealing with my shoulder injury.

"My doctor insists that I stay at home and heal it every single day so I can have a chance to play next year."