Top seed and defending champion Victoria Azarenka, who was to have played Wozniacki in the quarterfinals, withdrew due to a right ankle injury. Samantha Stosur, Kerber's opponent, could not play due to a strained right calf.
"On my warmup today I tested it out as much as possible," Azarenka said. "I tried absolutely everything I could to do, but I have been advised by the doctor, by my own team, that it's just a very, very high risk already.
"It's already really painful, but it's very high risk to make it much worse."
Azarenka had put together a 17-0 record this year before suffering the injury.
Stosur said she injured her calf muscle in the final game of her fourth-round victory over Mona Barthel.
"I don't know if you can get any more unlucky than that," Stosur said. "I love playing in front of this crowd, so to have to pull out without even being able to get on court is probably as bad as it gets."
Kerber and Wozniacki will face off in Friday's semifinals. Kerber has won three of their five career meetings -- all of those victories having come in 2012.