The Nadi facility was the first to apply to conduct Covid testing privately, Fong said.
"We have done site inspection and reviewed their processes and approved.
"Only one person is positive and he is linked to the first case.
"Zen Clinic gang are in quarantine. Zen is now setting up his lab with his own machine which he will operate after they finish quarantine."
At least 10 doctors and an administration staffer were part of what Fong explained was "a swab demonstration class done for Zen doctors" on May 29.
During the training exercise, the test swab was taken from the staff member who had reportedly shown flu-like symptoms.
"The swab then went back to our lab in Nadi for testing."
Fong said the swab returned a positive result and all the doctors present at the exercise were called in to quarantine.
On the same day, Prime Minister Frank Bainimarama announced that two positive cases had been detected after more than 14 days of being Covid-19 free.
Fong said GPs who acquire their own Covid-19 testing machines must consult Fiji's health ministry on testing protocols.
He said so far only one private GP had applied to conduct Covid-19 testing.
On Sunday afternoon, Zen's Medical Centre informed its patients and the public of the incident, saying staff had "come in contact with the Covid-positive case from Nawaka".
"After meticulous deliberation and consultation with MOH, we have temporarily closed the Nadi Clinic for today," a statement from Zen Medical stated.
"This is to allow the ministry to conduct a risk assessment and thorough decontamination/cleaning of the Nadi centre."
The clinic was given the all-clear to resume operations on Monday.
Navy cluster grows
Three more Fiji Navy officers have tested positive for Covid-19, bringing the total to 26 cases in the cluster.
The navy cluster continues to register the highest number of cases since the first naval officer was screened at a Ministry of Health outpost in Tamavua, outside the capital Suva, last week.
- RNZ