The club has confirmed the news, although they have not announced which coach has contracted the virus.
The announcement came just a few hours after the Newcastle Jets, who also play in the A-League competition, confirmed one of their players has also tested positive for Covid-19.
"The club is cooperating fully with all the relevant health authorities, and is focussed on supporting staff, as well as ensuring that all government protocols are being closely adhered to," they said.
"As per Ministry of Health instructions, all players and staff who had direct contact with the staff member are being monitored for possible signs of infection - any person showing symptoms consistent with Covid-19 will immediately be tested.
"The club will continue to monitor the situation closely and won't be making any further statement at this time."
News of the two cases within the A-League came after they were the last major sporting competition in the Australasian region to put their season on hold, announcing a suspension of all further matches on Tuesday.
The Phoenix had, at that point, completed six days of a 14-day quarantine in Sydney in the hope of playing their last six matches in Australia.
The non-Australian members of the Phoenix squad and travelling staff immediately returned to New Zealand and went straight into self-isolation.