She lost 6-4, 6-4 to Clara Burel of France, who is ranked 131st in the world.
Rybakina was seeded only 25th, with her victory in the most recent grand slam not boosting her in the rankings because no points were awarded at the tournament this year. The men's and women's tours took that step after the All England Club barred Russian and Belarusian players from competing because of the war against Ukraine.
Rybakina, who was born in Russia but represents Kazakhstan, said before this tournament she thought that was unfair, adding she didn't even feel like a Wimbledon champion.
Rybakina squandered six of the seven break points she earned in the first set as she racked up 19 unforced errors.
Former junior number one Burel capitalised on her chances to break in the fifth and ninth games.
Burel broke the Russian-born Rybakina in the opening game of the second set and won more than three-quarters of her first-serve points under hot and humid conditions on day two of the hardcourt major.
She thrust her fists in the air after clinching victory with a backhand winner.
World No.1 Iga Swiatek cruised through her first test at the US Open by swatting away Jasmine Paolini 6-3 6-0 at Flushing Meadows.
The Polish star is chasing a third grand slam title, and her second of the year after triumphing at the French Open in June.
Having held top spot in the rankings since April in the wake of Ash Barty's retirement, the 21-year-old is chasing her best result yet in New York, having reached the fourth round last year.
At Louis Armstrong Stadium on Tuesday she made an impressive start to her quest, with a near-flawless performance that saw her break Paolini seven times.
Swiatek is likely to face a more difficult challenge in the next round when she runs into 2017 champion Sloane Stephens, who battled back to see off Belgium's Greet Minnen 1-6 6-3 6-3 to the delight of the New York fans.
"I was just fighting as hard as I can and with your guys support, you pushed me through, so thank you," she said.
"Happy to get another win at my favourite tournament."
Joining Swiatek in the second round are American eighth seed Jessica Pegula, who beat Viktorija Golubic 6-2 6-2, and sixth-seeded Belarusian Aryna Sabalenka after her 6-1 6-3 win over Catherine Harrison.
Garbiñe Muguruza, seeded ninth, beat Clara Tauson 6-3 7-6 (7-5).
No. 22 seed Karolina Pliskova, the 2016 US Open runner-up, needed a third-set tiebreaker to edge Magda Linette, but No. 16 Jelena Ostapenko was ousted by China's Zheng Qinwen.
With agencies
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