Clutha Health First manager Ray Anton said a shortage of GPs in the town, which emerged several weeks ago, was only going to get worse.
With some doctors taking leave, August was going to be "a bit of a rough patch".
It could be up to seven days before people were seen by a doctor and Mr Anton asked that patients be "tolerant" of the delays.
"We don't have enough doctors and we are using locums to fill in the gaps, which is a short-term solution," he said.
The staff shortages began recently with the departure of three doctors, and had been compounded further by two doctors failing to arrive.
An Australian doctor was waiting to move across the Tasman while a Spain-based Russian doctor, who was due to start in May, failed the English test. It was hoped he would start early next year.
Clutha Health had been in discussions with three potential staff members, but one had been ruled out and discussions were still being held with the other two. Another doctor was to be interviewed on Monday.
It appeared New Zealand doctors were holidaying in warmer climates and it was hard to attract doctors from outside the area to come to Balclutha at this time of year, Mr Anton said.
Staff were eagerly anticipating the arrival of a specialist nurse at the end of August. West Coast nurse Gayle Lindley would work from 9am-6pm daily, dealing with urgent and "drop-in" work, which would free up the GPs.
She would be assisted part-time by long-serving ward nurse Julie McElrea.
Balclutha pharmacists are noticing an increase in the number of people seeking medical advice.
Unichem Grays Pharmacy owner Daniel Haw said while he could not quantify the number, there had been a "noticeable increase" since the doctor shortage began.
"... they are coming in for medical advice. We are seeing a bit of everything, from wounds and infections ... to people saying they can't get their children in till next week."
He said people running out of prescription medication were coming to the pharmacy, which was something Elwyn Bates Pharmacy owner Margo Roxburgh also reported.
"People on regular medication have been asked to approach the doctor ahead of time, and they are not doing that.
It does sometimes create a problem when people are running out of their tablets."
Mr Anton also advised people who needed repeat prescriptions or who had routine appointments to book well in advance.
"Don't wait till you are down to your last two pills to make an appointment with a doctor."
Until the staff shortage was overcome, Mr Anton asked non-urgent patients to give them leeway.
If the matter was urgent, patients would be seen by a doctor as quickly as possible, he said.
If it was highly urgent, Mr Anton advised people to call 111.
