The world number two Serena Williams has not played since losing in the US Open semi-finals in September and after consulting her medical team, she has been advised to rest in preparation for the 2017 season.
The 35-year-old 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.”
The absence of Williams has moved Great Britain’s Johanna Konta into the eighth and final spot for Singapore, but she is currently suffering from an abdominal injury.
Konta will miss out on the last place should Svetlana Kuznetsova or Carla Suarez Navarro win this week’s Kremlin Cup in Moscow.