"I am sadly unable to compete in this year's U.S. Open due to my ongoing family situation that I am working through," former world number one Azarenka, a finalist at Flushing Meadows in 2012 and 2013, said in a statement.
"While I will dearly miss being in New York and playing in one of my favourite tournaments where I have enjoyed some of the best moments in my career, I am already looking forward to being back next year."
Due to the custody battle, Azarenka is unwilling to leave her son behind in California, where she has a home and where her child was born.
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In an open letter posted on social media last week, Azarenka said no one should ever have to decide between a child and their career. She also said the only way she could play in the U.S. Open is if she left her child behind in California, which she was not willing to do.
Since returning to action, Azarenka has reached the last 16 at the Mallorca Open in June and Wimbledon.
Azarenka's withdrawal has opened up a place for Japan's Misa Eguchi in the main draw at the year's final grand slam.
(Reporting by Frank Pingue in Toronto; Editing by Neil Robinson and Pritha Sarkar)
