King is an American ranked 76th. She said she began to feel pain in her hip after the first set of a 6-1, 6-3 victory against Christina McHale 6-1, 6-3 on Thursday at the hard-court tournament that serves as a tuneup for the U.S. Open.
"I had quite a lot of pain yesterday and I was hoping that it would settle down, and that I would be able to play today," King said Friday. "But this morning, I didn't feel well enough to play."
King also pulled out of next week's tournament in Montreal but doesn't think the injury will prevent her from entering the U.S. Open, which begins Aug. 25.
"I don't think it's serious. I don't need a couple months off. I don't need surgery," King said. "I'm going to take off a couple days and see how it feels and then go from there."
Kuznetsova tweeted: "Sorry for V.King injury, hope you recover soon. Now to get ready for tomorrow."
In Saturday's semifinals, the No. 6-seeded Kuznetsova will face No. 2 Ekaterina Makarova, who beat No. 5 Anastasia Pavlyuchenkova 7-6 (3), 6-3. The other women's semifinal is Marina Erakovic of New Zealand against Kurumi Nara of Japan.