The Public Health Nurse was taken from the island by the Bunbeg coastguard late last night.
It is understood the man at the centre of the threats had been involved in an earlier dispute at his own house.
The nurse was accompanied from the island and was not hurt.
Gardai later arrived on the island and interviewed a young man but there have been no charges yet.
One local source said the nurse, who has worked on the island for a number of years and is very well liked and respected, was badly shaken.
“It is disgraceful that somebody would threatened the nurse like this. She is on the island for our benefit.
“Thankfully she has not been hurt in any way and that is the end of the matter.
“We would like the nurse to know that we are sorry for what happened to her and that we are looking forward to her coming back to us,” said the source.