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A man was killed and two people injured in the sudden storm, which left an estimated 1200 homes damaged, on Saturday.
"My heart goes out to the family and friends who have lost a loved one, and to those who have been injured," Acting Minister for Emergency Management Kris Faafoi said in a statement today.
"I know this has been a distressing weekend for people in Auckland, with many lives disrupted, and many homes and businesses damaged."
Council teams are going house to house to assess the damage.
"While it's too early to know the full cost of the damage, this initial contribution will help those communities start to get back on their feet," Faafoi said.
The money will be contributed to a mayoral relief fund to help the tornado victims.
"We will stay in contact with Auckland Council, which is contributing a similar amount to the fund, to see what further assistance may be needed as site assessments are completed in the coming days," Faafoi said.
"This funding is in addition to other support that people may be eligible for through the Ministry of Social Development."
Auckland Emergency Management has also set up a Welfare Centre at the Otara Pool and Leisure Centre.
People who need assistance but are unable to get to the centre can call Auckland Emergency Management on 0800 22 22 00.
"I'd like to recognise the extraordinary efforts of emergency management staff, first responders, volunteers, businesses, community leaders and residents who have also provided support," Faafoi said.
"There is still a recovery effort ahead for this impacted community. They should know the Government will be standing alongside them."