Win that, and Williams could face No. 2 seed Anett Kontaveit of Estonia in the second round.
The brackets for the women's and men's singles events were released Thursday by the U.S. Tennis Association.
Play begins Monday; first-round matches will be held that day and Tuesday. There was no immediate word on when Williams will compete.
The 23-time Grand Slam champion, who turns 41 on Sept. 26, announced this month she was preparing to step away from her playing career. She did not explicitly say when she planned to stop but made it sound as if the U.S. Open would mark her farewell.
Williams has won the hard-court tournament in Flushing Meadows six times.
She is just 1-3 this season, having recently returned to singles action after a year away following a first-round injury exit at Wimbledon in 2021.
Her first match back came at the All England Club in late June, and she lost her opener there in a third-set tiebreaker to 115th-ranked Harmony Tan.
Kovinic is a 27-year-old from Montenegro who is 80th in the WTA rankings this week and has been as high as 46th. Williams and Kovinic have never played each other in singles.
After winning a match at a tournament in Toronto, Williams was eliminated in straight sets there by Tokyo Olympics gold medalist Belinda Bencic, then lost again in straight sets at Cincinnati against reigning U.S. Open champion Emma Raducanu.
Because Williams has said she's preparing to wind down her tennis career, her every move will be the focus at the start of the U.S. Open.
While Williams has spent more than 300 weeks at No. 1, her lack of activity has contributed to a slide; she is 410th this week.
That meant she would not be seeded in New York and could have been placed anywhere in the field — and against any player.
Other possible opponents for Williams, should she progress through the tournament, include No. 27 seed Martina Trevisan of Italy in the third round and 2021 U.S. Open runner-up Leylah Fernandez of Canada or 2021 French Open champion Barbora Krejcikova of the Czech Republic in the fourth.
She could face her sister Venus only in the final, because they are on opposite sides of the bracket.