The go-ahead was finally given and a replacement doctor was left at the station as Dr Nielsen was taken aboard the rescue plane.
US Air Force Captain Victor Hines said: "The passenger exchange took just 22 minutes."
Click here to see a map of the rescue flight route
Dr Nielsen was the sole physician for the researchers at base - the same station where scientists discovered the hole in the ozone layer over Antarctica in 1986.
She had been treating herself with equipment dropped by a US military plane during an unprecedented emergency flight in July.
However, she was unable to use an ultrasound scanner after it was damaged during the operation.
The National Science Foundation, which runs the base, has refused to comment on Dr Nielsen's medical condition or whether breast cancer had been diagnosed.
Back-up plane
A second LC-130 aircraft had stayed behind at McMurdo Station as a back-up in case the rescue mission ran into problems.
The crews will not normally fly in temperatures less than -50 degrees - below that and the hydraulic and fuel systems are likely to seize up
The South Pole station is physically cut off from the world from February to October.