Robertson said the Ministry of Social Development (MSD) has been providing support to the Papatoetoe area.
He is asking anyone in the area who needs to, to get in contact with MSD.
He said there are some families where a disruption like this would cause them "significant concern".
The Government has budgeted $400-$500 million for the coming seven days, Robertson said.
Robertson denied that the Government was "yo-yoing" New Zealand out of lockdown.
Robertson said the Cabinet meeting on Saturday started at 7.45pm - he said it was a call.
On the Covid costs, Robertson said: "We have this buffer available".
Based on previous lockdowns Auckland level 3 and rest on NZ at level 2 cost the economy about $440 million a week, according to ASB.
Auckland Business Chamber CEO Michael Barnett said the business coommunity will be "bitterly disappointed to plunge back into alert level 3 lockdown.
"It is frustrating and a blow to recovery, but we will rally and accept the help put in place to save jobs," Barnett said.
"Businesses will be eligible for both the wage subsidy and the resurgence payments to mitigate some of the costs and liabilities from having to limit activities for the next week in such short order even though we all could see the warning signs.
"If you had a travel permit to cross the border from last time, it will still apply," he said.