Coastal ranger Jim Fyfe said there had been no sightings of the eight-day-old female pup's mother since its birth and it appeared the pup had been abandoned, which was unusual.
"Mothers will usually stay with their pup for the first week before heading back to sea to feed.
"It's possible that the mother has returned in the last day or so without being seen and without leaving any evidence," he said.
Mr Fyfe will continue to monitor the pup and compare its weight over several days to determine if it is receiving milk from its mother.
The pup is exposed and vulnerable to dog attack, but Doc is not considering moving it, in case the mother returns.
"The species in nationally critical, and pups are small and vulnerable to dogs and other disturbances."
Signs have been in place this week warning dog owners to keep their animals under strict control in the area.
Doc also asks beach-goers to report any sightings of the pup's mother, or any other injured or at-risk wildlife, to 0800 DOC HOT (0800 362-468).