The former world number one has not featured since Wimbledon and was forced to withdraw from the US Open for legal reasons.
She has featured only twice since her return to the tour before the custody judge ordered that her son, Leo, cannot leave the state of California.
‘Work to resolve some of the legal processes’
She was forced to withdraw from the US Open after a court order prohibited Leo from leaving the state of California.
“As we work to resolve some of the legal processes, the way things stand now is that the only way I can play in the US Open this year is if I leave Leo behind in California,” she wrote on Twitter in August.
“Balancing child care and a career is not easy for any parent, but it is a challenge I am willing to face and embrace.
“I want to support men and women everywhere who know it is OK to be a working mother - or father. No one should ever have to decide between a child and their career, we are strong enough to do both.
“I look forward to hopefully having positive developments soon so that this difficult situation can be resolved and I can get back to competing.”
Missing the final will be an especially tough blow for Azarenka considering it will be Belarus’ first-ever Fed Cup final.
They will square off against this year’s US Open champion Sloane Stephens and Coco Vandeweghe, as well as Shelby Rogers and Alison Riske.
19-year-old Aryna Sabalenka, a finalist in Tianjin, will now headline the Belarus side, alongside Aliaksandra Sasnovich, Vera Lapko, and Lidziya Marozava.