As is usually the case with Williams, there is a lot at stake. There is no Grand Slam to tantalize her, but if she wins the Open, she will pass Steffi Graf with her 23rd major tournament victory, an Open era record. She would also pass Chris Evert for the most United States Open singles titles with seven. At the same time, she is fighting to maintain her long hold on the No. 1 ranking.

Last week, Williams went to Cincinnati intent on protecting her No. 1 ranking against an assault by Angelique Kerber, who is No. 2. But after an uncomfortable practice there, the aching shoulder forced Williams to withdraw.

Kerber could have passed Williams in the rankings if she had won in Cincinnati, but Kerber lost in the final to Karolina Pliskova. Depending on how each fares at the United States Open, Kerber can still end Williams’s reign at No. 1. Williams has held the top spot for 184 consecutive weeks, two short of Graf’s record.

Williams was handed a challenging first-round matchup against Ekaterina Makarova, ranked No. 36. Williams holds a four-to-one advantage over Makarova, who beat Williams at the 2012 Australian Open. They also met in the semifinals of the 2014 United States Open.

Williams said her shoulder was starting to feel better, but that she was trying to balance the need for rest with the need to practice.

Her coach, Patrick Mouratoglou, said he did not believe that the shoulder would hamper Williams’s pursuit of her 23rd Grand Slam singles title, which would leave her one short of Margaret Court’s overall record.