The former Wimbledon champion, a three-time finalist in Cincinnati, underwent a scan on the leg injury she suffered during her second-round victory against Magda Linette which revealed a small tear in her right adductor.
Romanian Halep faces a race against time to be ready for Flushing Meadows, which begins in 12 days.
A month after beating her on the grass at Wimbledon, Tunisia’s Ons Jabeur picked up another win over Poland’s Iga Swiatek, a 6-3 6-3 victory in just 78 minutes.
It was a straightforward victory for the Australian, winning 6-4 7-6 in an hour and 46 minutes.
Naomi Osaka fought back from a set and a break down to beat American teenager Coco Gauff and will meet wildcard Jil Teichmann in the round of 16.
Former world number one Angelique Kerber picked up a notable win over Elina Svitolina.
The German won 7-5 2-6 6-4 after Svitolina had won their previous seven matches.
There was a surprise late in the day when third seed Aryna Sabalenka was beaten 5-7 6-2 7-6 (4) by Spain’s Paula Badosa.
Victoria Azarenka secured a straight-sets victory over Alison Riske but 13th seed Jennifer Brady had to retire hurt with Jelena Ostapenko progressing instead.
Petra Kvitova, ranked 11th for the tournament, won 6-2 6-4 against Veronika Kudermetova.
Seeded players Elise Mertens and Bianca Andreescu fell to defeats to Elena Rybakina and Karolina Muchova respectively.
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