"As we continue to provide ongoing support to our team member and to maintain confidentiality, we will not be providing any further details," the spokesperson said.
"We have no information to suggest another team member or passenger has tested positive for Covid-19, and do not track Covid-19 related information on our customers."
The Herald could not get clarity on whether Fullers staff operate in work bubbles to prevent the entire ferry fleet being out of action if workers had to isolate on a large scale.
The Fullers spokesperson merely reiterated that they have "a robust Covid-19 Pandemic Response Plan in place and have prepared for several scenarios".
However, the Fullers spokesperson did say they had to balance Covid-19 risks with keeping Auckland's ferry commuters moving.
"We are acutely aware of the risks of Covid-19 and balance those risks against our commitment to keep Auckland moving through the provision of a reliable and safe public transport and tourism service. This includes how we manage shift work and rostering on our vessels," Fullers said.
"We have closely followed the Ministry of Health and WorkSafe guidelines and are confident our Pandemic Response Plan measures are robust and being followed."
Maritime Union Auckland secretary Russell Mayn said they were aware of the positive Covid-19 case, but were comfortable that the risk to other Fullers workers was "extremely minimal" as claimed.
Mayn said the union supported proactive Covid-19 testing for staff where appropriate, and understood Fullers staff were working in bubbles under level 4 restrictions, but not now.
"With the state of the [Auckland Harbour] bridge you wouldn't want the ferries out would you?" Mayne said.
"But it does highlight how vulnerable our infrastructure under these sorts of things is if the bridge is damaged."
Fullers is a ferry company in Auckland which operates in the Hauraki Gulf and Waitemata Harbour.