The Government today committed to an April 1 deadline for increasing minimum wage to $20 to deliver on Labour's election promise and the commitment from the last Government.
It's expected to give 175,000 workers a $44 weekly pay rise before tax.
Wood said the increase was signalled years earlier and Labour was elected with a strong mandate "to deliver on our promises".
"This increase will lift the incomes of thousands who will then go on to spend a good chunk of their wages at local businesses."
Wood said MBIE's annual review of minimum wage and its recommendations on raising it was based off economic data "that is now out of date".
The MBIE advice was compiled at the start of December ahead of Treasury opening its books this week to reveal New Zealand's economy had fared better than expected.
Its advice recommending a more gradual approach and increasing it from $18.90 to $19.15 was primarily based on the Pre-election Economic and Fiscal Update in September which cast a much darker picture of the Covid economic hit.
It advised that the rise should happen on October 1 because that was what the forecasts at the time indicated unemployment numbers would start to recover.
"The economic situation, consumer caution and future uncertainty around trading conditions mean that employers may not be able to recover increased wage costs through normal responses such as reducing profit margins or increasing prices," officials said in the advice.
"The end result could be that the workers who would benefit the most from a minimum wage increase are the ones most likely to experience the negative effects of an increased minimum wage (such as reduced work hours or the substitution of some groups of workers for others)."
But by opting to increase it to $20 instead of $19.15 would mean about 70,000 more workers were likely to benefit.
And it would have a positive impact on actual day-to-day living conditions of some low and middle-income families and would contribute to reducing material hardship.
It said the timing of a minimum wage increase was "an important consideration in this year's decision".
MBIE said previous minimum-wage increases were cushioned by new jobs being created in the economy but Covid-19's impact meant the increase to $20 in April "would be unaffordable for some businesses".
"This risks increasing unemployment or underutilisation for low-paid employees, particularly those people on or near the current minimum wage."
Treasury has employment growth recovering by the year to June 2022 to deferring the rise until October would align the change "with a potential upturn" and might mitigate the risk of employers letting staff go, or reducing hours.
"This proposal would give employers much-needed breathing space and enable those most affected by the downturn in trade to recover and retain their staff until the economic situation improves."
But it did not advise for there to be no increase as that would "erode the real incomes of the lowest-paid workers compared to wage growth and inflation".
Increasing the minimum wage would have the biggest impact on workers who are young, female, Māori, Pasifika, part-time employees, without formal qualifications, or working in the retail and hospitality industries.
This group was also the most likely to experience job losses and reduced hours.
This could be mitigated by Government interventions like job subsidies, job creation, employment support or other initiatives.
Act leader David Seymour called the wage increase "economic vandalism" and said businesses "simply won't be able to keep up with the constant stream of costs and rules being imposed by Labour".