Wozniacki progressed after defending champion Victoria Azarenka withdrew with an ankle injury, while Kerber's opponent Sam Stosur pulled out with a calf problem.
Both Stosur and Azarenka withdrew after testing their injuries in warm-up sessions, leaving Kerber and Wozniacki with free routes through to the last four.
"On my warm-up today [Thursday] I tested it out as much as possible," top seed 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. I mean, it's already really painful, but it's very high risk to make it much worse."
Stosur suffered her calf problem in the last game of a three-set win against Mona Barthel on Tuesday and iced her leg instead of taking part in practice on Wednesday.
"I don't know if you can get any more unlucky than that," Stosur said in a statement. "I think we only played another four points in that match. I felt something go in my calf and it was hurting a fair bit.
"Yesterday (Wednesday) I took the day off practice and only did treatment, probably iced it about 10 times. This morning I thought I would give it a shot and tried to go out and warm up.
"After about five minutes, I knew that there was no chance I could play unfortunately. I think this is only the second time I've ever pulled out of a match in my career."