Three wards at Southland Hospital in Invercargill have closed their doors to visitors because six cases of Covid-19 were confirmed.

Dr Hywel Lloyd who leads the Southern DHB's Covid-19 response said two patients, one on the rehabilitation ward and another on the medical ward, both tested positive on Friday followed by two more, one in each ward.

Two patients on the surgical ward have also since tested positive, he said.

There are restrictions in other areas of the hospital also with those needing medical assistance from the ED limited to having one support person.

A woman who spoke to RNZ said her 96-year-old grandmother died in the hospital with no family by her side.

The woman who RNZ has agreed not to name understood that measures needed to be introduced to safeguard others during the pandemic, however, "turning a hospital into prison is not the way to go about it".

People recovered if they had the "love and positivity" of family, she said.

She also complained of being interrogated while trying to visit her terminally ill mother-in-law who is a patient at the hospital.

Dr Lloyd said the woman's experience with her grandmother was "an incredibly sad difficult situation" and the hospital appreciated the positive influence whānau provided during hospital visits to their relatives.

"We don't do this lightly. We've got significant pressures to ensure that our patients remain safe and we need to ensure that our staff don't get infected because we've got significant staffing shortages and to maintain the care for our in-patients is paramount for us."

Responding to complaints that families were being interrogated while trying to visit patients, he said that was unacceptable.

Logistically it would be time-consuming and "incredibly difficult" to administer a rapid antigen test to every potential visitor.

The hospital is unsure if a visitor or staff member has introduced the infection. The region still has high numbers of cases and inquiries into the source are continuing.

During the lockdown the hospital is trying to provide as much contact as possible between patients and families via Zoom or Skype or other technology.

Dr Lloyd said some patients are due to be retested and a decision will be made on Thursday whether the lockdown can be lifted.