Both Robertson and Prime Minister Jacinda Ardern had said they were monitoring economic activity and referred to the possibility of targeted support.
Robertson described latest payments as "targeted" but businesses of any type can qualify for the payment if they meet the revenue test.
Businesses can apply for the first payment from February 28 and payments start from March 1.
The payments were broadly welcomed by business groups, but there are warnings that many businesses will struggle to meet the test.
Auckland Business Chamber chief executive Michael Barnett said the payments would be a "lifeline" for many small businesses.
"Government has listened and recognised the plight of hard-hit businesses to meet their costs and hold onto staff as the pressure builds along with Omicron's surge," Barnett said.
"The three $4000 payments plus $400 for each [full-time employee] over the six-week period will cover, we estimate, up to 70 per cent of an average SME's outgoings."
Marisa Bidois, chief executive of the Restaurant Association said many hospitality businesses were "bleeding cash" at the moment.
While she welcomed the payments "we would like to have seen the threshold slightly lower at 30 per cent, to reflect the average losses our members are reporting and more fairly reflect the accumulative effect of the revenue drops which members are experiencing year on year."
Hospitality NZ chief executive Julie White warned the payments were small compared to the losses being faced by the sector. After raising concerns with the government for weeks, at least businesses had certainty about the amount of support available.
"It looks like it will not be enough. Many will now close, or at best hibernate. Either way, it means job losses," White said.
Payments could be extended
The payments are available on a fortnightly basis for six weeks – three payments in total.
Robertson said that reflected the expected timing for Omicron to peak and ease again.
"We will continue to closely monitor the situation and have the option to extend the payment if this is necessary," Robertson said.
The Treasury estimated that the cost of each payment will be $160m-$260m.
The government had been monitoring the impact of the traffic light system on businesses and the economy, and while most businesses could open and operate relatively normally there had been drop-offs in business for many.
"We can see that the majority of the economy is operating close to normal, but in some sectors, like hospitality and events, there has been a significant drop-off in business. There are a range of reasons for this, but it is clear that the impact is putting a number of viable businesses at risk of not being able to operate."
Robertson said the higher revenue loss threshold was to target those most affected.
"We looked closely at whether we could offer sector-specific packages but the definition of who is in what sector, and the need for cash flow to be provided quickly meant that was not a feasible option to reach the most affected," Grant Robertson said.
Revenue Minister David Parker said changes were also being made to the Small Business Cashflow Loans Scheme to increase the amount of funding available to eligible businesses through the introduction of a "top-up" loan.
