Victoria Azarenka has picked her baby over the US Open -- officially pulling out of the upcoming tennis tournament because she refuses to his leave the state without her 8-month-old son. 

As we previously reported, Azarenka is in the middle of a nasty custody war with her baby daddy, Billy McKeague -- who hit her with court docs in L.A. The judge has ruled Azarenka can not take her kid out of the state until the trial is over -- which ain't gonna happen for a while. 

The US Open begins next week in New York -- and rather than leave the baby's side for 2 weeks, the former #1 womens player has withdrawn completely. 

"I am sadly unable to compete in this year's US Open due to my ongoing family situation that I am working through," Azarenka says.

"While I will dearly miss being in New York and playing in one of my favorite tournaments where I have enjoyed some of the best moments in my career, I am already looking forward to being back next year."