Barty could come up against Iga Swiatek in the last eight and Karolina Pliskova if she makes it through to the semi-finals at Flushing Meadows.
Simona Halep's encounter with Camila Giorgi is a mouthwatering first-round match, while defending champion Naomi Osaka returns to grand slam action against former US Open junior champion Marie Bouzkova.
Angelique Kerber could be a tough fourth round opponent for Osaka. Close friends Madison Keys and Sloane Stephens meet in another eye-catching first-round match.
There will be no Serena or Venus Williams at the final Major of the year because of injuries to both.
French Open runner-up Tsitsipas and 2012 champion Murray is one of the standout matches in the opening round of the men's draw.
No.1 seed Novak Djokovic will start his quest for a calendar Grand Slam against a qualifier in New York and could face a repeat of the Wimbledon final versus Matteo Berrettini in the last eight.
World No.1 Djokovic, a strong favourite for a record 21st Major title with Rafael Nadal and Roger Federer absent because of injury, could do battle with Alexander Zverev at the semi-final stage.
Daniil Medvedev, the No.2 seed, is in the bottom half with Tsitsipas, who he could come up against in the semi-final. Medvedev's first test will come against Frenchman Richard Gasquet.