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The 47-year-old man was given a pre-charge warning, according to Stuff.
Police said the man, who had tested positive for the virus, had been shopping at the Browne St Countdown on Wednesday.
It's not clear when he was tested or whether he was showing symptoms during the grocery shopping expedition.
Under lockdown rules, any breach of the Covid-19 guidelines, which include that anyone confirmed to have the coronavirus must self-isolate for 14 days, can incur a $1000 fine.
New Zealand has recorded 11 deaths from Covid-19 and more than 1400 cases at 1pm yesterday. More than half of those infected with the virus have now recovered.
Seven of the deaths relate to a Canterbury rest home cluster of residents aged in their 70s, 80s and 90s with underlying health conditions.
The Alert Level 4 lockdown is in place until the end of Wednesday. The Government is expected to advise on Monday whether or not it will drop to Level 3 after that.