The walkover sees No.5 seed Daria Kasatkina progress to Saturday's decider, to face the winner of Belinda Bencic and Veronika Kudermetova.
The world No.11 is hopeful of playing at the Australian Open, which begins on Monday in Melbourne.
"I'm really disappointed that I had to withdraw today because I was really looking forward to the match," Badosa 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 to win 74 and 81-minute sets in Thursday's gruelling quarter-final.
"Yesterday when I was playing against (Beatriz Haddad Maia), 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.
"Today I feel a little bit worse, so yeah, I have the Australian Open ahead, and I hope I can recover for that.
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