"If you know anything about its whereabouts, please contact the police," he added.
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Chief Executive Officer of East Health Trust Loretta Hansen said staff first noticed the tent was missing early this morning.
"They arrive much earlier than the time the testing station opens at 8am."
The missing tent, which was made with galvanised steel and a heavy duty PVC cover, had been bolted to the ground and was the middle one in a set of three.
The police are investigating and "are pretty keen to catch" whoever was responsible, she said.
"We thought 'we are not going to let this stop us from testing'. People have been fantastic."
A staff member was able to quickly set up a temporary marquee to ensure they had a covered area, but not long after the original installers replaced it with a new testing tent.
Hansen said while they would like the original back it was hard to know what kind of condition it would be in.
"It is very difficult to know what they think they are going to use it for," she said.
"It is really disappointing when you are in the middle of a crisis like we have got and then you have got some Wally that comes along and pinches your tent from a testing station."
It comes as the number of confirmed and probable cases of the virus in New Zealand rose to 589 yesterday.
Auckland has the greatest number of those cases, recording 209.
Covid19.govt.nz: The Government's official Covid-19 advisory website