The area, that involves the counties of Caithness and Sutherland, is short of eight consultants at its local hospital and also needs to find more GPs.
Frank Stephen, of Thurso's Riverbank Medical Practice Patient Participation Group, told of the public concerns.
Health Secretary Shona Robison said she was confident NHS Highland was taking steps to address recruitment problems.
Ms Robison led the meeting in Wick which served as an annual review of the health board's performance.
During the meeting, Mr Stephen said people in Caithness believed health care in their area was on the brink of meltdown.
Later he told BBC Alba: "People are really concerned that it is on the precipice.
"There is a shortage of consultants. There seems to be a failure to attract consultants to the local area.
"And there is a shortage of GPs within the county. At my own practice we are three GPs short."
Ms Robison said the recruitment of specialists was a global challenge and not unique to Scotland.
Following a visit to Caithness General, she said patients were being offered proper care.
She said: "I would say it is a good, well performing hospital with dedicated staff.
"People going into that hospital should be assured that there is a very good safe service on offer."
Last month, the training of junior doctors at the far north's main hospital, Caithness General in Wick, was temporarily suspended.
It followed the resignation of a senior member of staff who helped in supervising the trainees.
NHS Highland and NHS Education for Scotland said they had taken the "difficult decision" to halt training.
The General Medical Council said it had "serious concerns" about staffing levels and the safe supervision of the trainee doctors.
Four trainee doctors were thought to have been due to start at the hospital.
A review of NHS Highland's performance has heard public fears that care in the far north is 'on brink of meltdown'.