The Herald reader who sent the screenshot to the Herald says the message was sent at 10.40pm on Saturday.
Contacted by the Herald, the Ministry of Health explained the contact tracing team sends a text message to outline that the contact comes from the Ministry and that text is sent in advance, to let people know they will be receiving a call from a specified 09 number within half an hour.
The official text message from the Covid-19 contact tracing team never requests a call back.
The Ministry of Health also includes information about the contact tracing calls on its website.
Anyone who is identified as a close contact of someone who has tested positive for Covid-19 can expect to be contacted by the MOH or the local District Health Board's Public Health Unit (PHU).
"The Ministry call centre staff will identify themselves and inform you that they are calling from the National Close Contact Service. They will also verify your name and contact details. These calls from Ministry call centre staff will usually come from 09 801 3009 and 09 801 3010," the website explains.
"Following this initial phone call, your details may be passed on to Healthline who will make follow up calls during your isolation period to check how you are doing. The calls from Healthline will usually come from 09 302 0408.
"There may be a delay before your call is connected. If you are concerned that a call from Healthline isn't genuine, you can email Healthline and request a call back."
Restaurant Brands, who owns Pizza Hut in New Zealand, says they had no knowledge of that text circulating until they were contacted by the Herald.
They said they have now liaised with the MOH about it and reported the text message to Netsafe.