Second seed and defending champion Novak Djokovic, who beat Medvedev in last year's final, is in the same half as German Alexander Zverev.
The draw raises the prospect of a possible semi-final clash between Sinner and Alcaraz who in 2022 produced an epic five-hour 15-minute quarter-final which concluded at 2:50 a.m.
Spaniard Alcaraz won that battle and went on to win his first US Open title.
But to reach a rematch with Alcaraz, Italian Sinner may need to get past 2021 champion Medvedev in the quarter-finals.
The 23-year-old Sinner heads to New York under a cloud after he was cleared of any wrongdoing after twice testing positive for a banned substance earlier in the season.
Sinner had explained that the substance had originated from a spray, containing clostebol, that had been used by a member of his staff to treat a cut finger.
The International Tennis Integrity Agency (ITIA) accepted the explanation and said the "presence of the substance was not intentional".
"I will now put this challenging and deeply unfortunate period behind me," said Sinner in a statement published on X.
Power-hitting Chilean Nicolas Jarry, the 26th seed, is the first seeded opponent Sinner could face. Jarry won their only meeting in 2019 in 's-Hertogenbosch.
Djokovic will start against a qualifier and then play either fellow Serb Laslo Djere or Germany's Jan-Lennard Struff.
Djokovic, a four-time US Open winner, is bidding to clinch a record 25th Grand Slam title.
Last year's US Open semi-finalist, Ben Shelton, will begin his bid against 2020 champion Dominic Thiem who is playing his final year on tour before retirement.
In the women's draw, world number two Aryna Sabalenka and defending champion Coco Gauff have been drawn in the same half and could meet in the semi-finals.
World number one and 2022 champion Iga Swiatek's highest ranked potential semi-final opponent is fourth ranked Elena Rybakina.
The highlight match of the opening round sees four-time Grand Slam title winner Naomi Osaka, the champion at Flushing Meadows in 2018 and 2020, face number ten seed and 2017 French Open winner Jelena Ostapenko.
The clash will be Osaka's first at the US Open since becoming a mother.
Fifth-seed Italian Jasmine Paolini, this year's French Open and Wimbledon runner-up, plays 2019 champion Bianca Andreescu of Canada.
Sixth seed Jessica Pegula, fresh from her run to the final in Cincinnati and title in Toronto, is drawn in Swiatek's quarter.
Pegula opens against compatriot Shelby Rogers and should she progress will face a former Grand Slam winner in the second round -- either Emma Raducanu, US Open champion in 2021 or Sofia Kenin, the 2020 Australian Open champion.
