"City Medical in Napier was closed on Sunday night due to staff illness and again on Monday during the day, due to illness impacting already critical staffing levels."
The statement urged people to take steps to ensure they can deal with minor ailments at home to alleviate stress on health providers.
Dr Jones said most people with Covid-19, influenza or other respiratory illnesses would be able to manage at home by resting, keeping up their fluids and taking paracetamol or ibuprofen.
"Good habits like washing our hands and wearing a face mask indoors can help to reduce further spread of the virus in the community."
Dr Jones said vaccination against both Covid-19 and influenza remains the best defence against serious illness for both adults and children and that this winter could see high levels of flu cases if people do not get vaccinated.
He said people should take a Covid-19 test if they had cold or flu-like symptoms, especially if they were a household contact of a positive case.
People can order RAT kits through the website https://requestrats.covid19.health.nz/.
"Make sure to record your test result at https://mycovidrecord.health.nz/ to ensure you are provided with the necessary health and welfare supports."
HBDHB chief operating officer Chris Ash urged people to seek advice about their healthcare early to avoid minor health issues presenting to ED, and more urgent situations becoming an emergency.
"If it's not an emergency, call Healthline on 0800 611 116, your pharmacy or your GP. We encourage people to use the hospital's emergency department for emergencies only, as priority will always be given to those with life-threatening conditions," Ash said.
People should see a doctor immediately if they have:
•difficulty breathing or chest pain
•a high temperature that does not come down with paracetamol or ibuprofen
•chills or severe shaking
•abnormal skin colour, is blue, or has a purple spotty rash
•seizures or convulsions
•are coughing up blood
•have stopped passing urine.
Meanwhile Hawke's Bay had 133 new Covid cases on Monday.
Nationally there were five deaths, 5836 new community cases and 403 current hospitalisations reported by the Ministry of Health on Monday.