A German woman who fell down a crevasse and broke two limbs while climbing a remote New Zealand glacier was rescued early Friday, police said.

They said the woman, described as an experienced mountaineer, slipped down a crevasse on the South Island's Fox Glacier on Thursday afternoon and her companion, a doctor, climbed down to secure her safely to the ice face.

He then raised the alarm and a three-person rescue team reached her on Thursday evening but conditions meant they could not move her so they stayed with her overnight.

"This morning's rescue went well and the rescue teams are now making their way off the mountain," rescue coordinator Sergeant Sean Judd said.

The woman, who was described as being very cold and in a lot of pain, suffered a broken leg and arm, as well as possible other injuries.

Police said the rescue team would fly the woman to the township of Franz Josef from where a helicopter would airlift her to hospital in Christchurch.