The 28-year old missed the US Open in August and has not played since July.
"Unfortunately, my current custody situation is keeping me in California," she said.
"It is heartbreaking for me to not have a chance to help Belarus in the final.
"My heart is always with my country and my team and I will cheer them from afar."
"I won't return until I'm 100% fit"- Murray
Wawrinka back in training after injury
In her absence, Belarus, who are competing in the final for the first time, will rely on world number 78 Aryna Sabalenka, aged 19, to lead their campaign.
"It's a pity but we just can't change anything right now," said Belarus captain Eduard Dubrov.
The United States, who are without both Serena and Venus Williams, have selected US Open champion Sloane Stephens, Coco Vandeweghe, Shelby Rogers and Alison Riske.
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