Spain's world No.11 Badosa pulled out of Friday's match against fifth seed Daria Kasatkina with a thigh injury.
World No.9 Kudermetova then followed suit, opting not to play against Belinda Bencic because of a left hip injury.
It means Kasatkina and Bencic will go head-to-head in Saturday's final.
Badosa said she remained hopeful of playing at the Australian Open, which begins on Monday.
"I'm really disappointed that I had to withdraw because I was really looking forward to the match," she said.
"I think I was playing very good tennis, high level. I played three really good matches. I think that helps me, as well, on my confidence for the tournaments ahead.
"Now it's something that I cannot control, so it is what it is."
Badosa battled through a gruelling quarter-final on Thursday against Brazil's Beatriz Haddad Maia, which featured 74 and 81-minute sets.
"It was a very tough match, especially physical, so I felt a little bit in my abductor," she said.
"I felt like I pulled it a little bit. (On Friday) I feel a little bit worse, so yeah, I have the Australian Open ahead, and I hope I can recover for that."
Kudermetova was coming off a three-set victory over Danielle Collins that lasted two hours 48 minutes.
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