Serena Williams has gone into labor and is set to give birth any minute ... and of course it's all going down in the middle of the U.S. Open!

The 35-year-old superstar was admitted to St. Mary's Medical Center in Palm Beach, FL on Wednesday and she was induced on Thursday evening, according to CBS12

Williams is all set for the big moment -- in fact, she and baby daddy Alexis Ohanian went on a grocery run recently to make sure her house is all stocked up and ready to go when she comes home with the kid!