The National Trust for Scotland (NTS) said the rarely seen Sowerby's beaked whale and its calf became stranded in the shallow waters of Village Bay, Hirta on Thursday, September 12.
Staff from the NTS and QinetiQ tried to refloat the animals but were unable to successfully move the mother before it passed away.
The calf managed to free itself and swam into open water but, without its mother, NTS said it was unlikely to survive.
The Sowerby's beaked whale is rarely-seen and very little is known about it. The species is thought to inhabit the deep offshore water in the North Atlantic ocean. There have been around 60 recorded strandings of the species around the UK in the last 24 years.
Gina Prior, NTS Seabird and Marine ranger, said: "The loss of such an enigmatic creature is massively unfortunate, particularly where the calf has been left orphaned, but the post mortem has provided a rare opportunity to learn more about an animal that is difficult to study in the wild."
Nick Davison, coordinator of the Scottish Marine Animal Stranding Scheme, said: "There have been 41 records of this species stranding around the Scottish coasts since 1989 nearly all on the West coast and quite a few from the Western Isles. It is one of the beaked whale family and almost all we know about this species comes from examining stranded animals. So it is vitally important to perform post mortem examinations on these animals if at all possible when they strand. Not only can we try and establish a cause of death but also gain insight into their life histories. It is not common for this species to strand alive in the UK, the fact that this was a mother and calf pair live-stranding was even more unusual. Hopefully tests on the samples taken at the post mortem will shed light on why this animal live stranded."