The 27-year-old produced a dominant performance to dethrone two-time defending champion Aryna Sabalenka in last weekend's US Open final, securing a third Grand Slam title to go with her rise to the top of the rankings.
An ankle injury had threatened to derail Rybakina's campaign before the tournament began, but she overcame those concerns to add the US Open crown to her Australian Open title this year and her 2022 Wimbledon triumph.
"I have to announce that I won't be able to participate in Billie Jean King Cup this year," Rybakina wrote on Instagram. "Am very sad to miss Shenzhen, such a nice place with an amazing crowd.
"Last month has been tough for my body and I will need to recover and be at my best to compete again. I wish girls good luck."
The Billie Jean King Cup Finals will be held in Shenzhen, China, from September 22 to 27, with Kazakhstan set to face Spain in the quarter-finals on September 23.
Italy are the two-time defending champions.