The complete figure was likely to be higher than the RIS had forecast as only the aforementioned ministries had said the wage hike would have a material impact.
But Clark said it was not expected to be a significant cost.
Raising the minimum wage from $15.75 an hour when the Government took office, to $20 an hour by April 2021, was part of Labour and NZ First's coalition agreement.
In December last year, Workplace Relations Minister Iain Lees-Galloway announced the minimum wage would be hiked to $17.70 an hour on April 1 this year.
National Workplace Relations and Safety spokesman Scott Simpson said the minimum wage increase would start to hurt people as the economy "continues to slow".
As the minimum wage progressively increases, it is likely it would continue to cost the Government more money.
Asked how much the planned minimum wage increase to $18.90 in 2020 and then $20 in 2021 would cost the Government, Clark said he did not know.
"We do not currently hold this information as actual payroll data is used to develop estimated costs to Government."
But he said the Government provided an early signal of their intentions for future minimum wage increases to give businesses greater certainty and allow for informed investment and business planning decisions.
"MBIE will still undertake a review each year so that the economic and other conditions at the time can be taken into account before a new rate takes effect, and will estimate the costs for Government at that time."