Chancellor said the move - worth up to a maximum of £2,500 a month - would cover 95% of self-employed workers and was an “unprecedented” gesture to cover the impact of coronavirus.
But the payments, while welcomed, have been described as having a “huge sting in the tail for millions of self-employed and freelancers” because of the potential delay.
The package comes after the Government came under sustained pressure as its initial package of financial support only covered employees.
Mr Sunak said: "To support those who work for themselves, today I am announcing a new self-employed income support scheme.
"The Government will pay self-employed people who have been adversely affected by the coronavirus a taxable grant worth 80% of their average monthly profits over the last three years, up to £2,500 a month."
The Chancellor said the scheme will be available "no later" than the beginning of June.
It is open to anyone with trading profits of up to £50,000 and will only be available to those who make the majority of their income from self-employment so only the "genuinely self-employed" benefit.
"And to minimise fraud only those who are already in self-employment who have a tax return for 2019 will be able to apply," he said.
"95% of people who are majority self-employed will benefit from this scheme."
The Chancellor said "it provides an unprecedented level of support for self-employed people".
But Labour MP Stephen Doughty said: "What are millions of people supposed to do until June, not least when there's a five-week wait for universal credit? How do they put food on table and pay their bills?
"This is a big announcement but with a huge sting in the tail for millions of self-employed and freelancers.
"The Government must urgently bring this scheme forward much more sooner so that livelihoods are not put at risk.
"Most people simply don't have the cash reserves in their bank accounts to get through one month, let alone three - and not least while banks have just racked up overdraft charges."