Speaking in the House of Commons, Mr Sunak said there was likely to be a significant but temporary disruption to the economy with the possibility of up to a fifth of the working age population off sick at any one time.
He said fiscal actions would be taken by the Government to complement the Bank of England's slashing of interest rates to 0.25 per cent and pledged a £30bn fighting fund to help the NHS, businesses and workers.
He said the NHS will receive "any extra resources it needs", whether that is "millions or billions of pounds" to deal with Covid-19 on top of £6bn of new funding to support the NHS over this Parliament.
The scale of the challenge facing the economy was underlined by the Office for Budget Responsibility (OBR) in forecasts prepared before the full impact of the virus could be known.
Growth is expected to fall to 1.1 per cent in 2020, down from 1.2 per cent last year, dramatically lower than the OBR's previous estimate of 1.4 per cent and marking the weakest expansion since the 2009 recession.
Mr Sunak said: "Taken together, the extraordinary measures I have set out today represent £7 billion to support the self-employed, businesses and vulnerable people.
"To support the NHS and other public services, I am also setting aside a £5 billion emergency response fund - and will go further if necessary.
"I know how worried people are. Worried about their health, the health of their loved ones, their jobs, their income, their businesses, their financial security.
"We will get through this - together. The British people may be worried, but they are not daunted."
Statutory sick pay (SSP) will be extended to all of those eligible and asked to self-isolate, even if they are not showing symptoms, and the Government will meet the cost for businesses with fewer than 250 employees of providing SSP for 14 days.
It will also create a £500m hardship find for local authorities to support people in their areas.
A temporary Coronavirus Business Interruption Loan Scheme will be introduced for banks to offer loans of up to £1.2m to support small and medium-sized businesses with their cash flow.
Business rates for businesses with a rateable value below £51,000 will be scrapped this year to support small businesses during the Covid-19 outbreak.
And the discount will be extended to the leisure industry for this year they will have 100 per cent retail discount.
Outside of the measures taken to combat coronavirus, the National Insurance threshold will increase from £8,632 to £9,500 and the National Living Wage will rise to £10.50 per hour by 2024 if economic conditions allow.
Fuel duty will be frozen for another year, £26bn will be invested in roads, and the Government will abolish £2.4bn annual tax relief on red diesel in two years' time, but agriculture, rail, domestic heating and fishing will be exempt.
Duties will be frozen on beer, cider, wine and spirits, and the Government will provide £1m to support Scottish food and drink overseas to combat US President Trumps' import tariffs. It will also give £10m to help distilleries "go green".
For business owners, the lifetime limit for entrepreneurs' relief will be slashed from £10m to £1m, saving the Government £6bn a year, but research and development investment will be increased to £22bn a year.
But Mr Sunak said "most of that money" will go back to firms through a series of other measures: increasing the tax break for research and development expenditure, the structures and building allowance and increasing the employment allowance by a third to £4,000.
There were promises of more support for start-up businesses and more investment in research and development would be increased to £22bn and £800m for a new "blue-skies funding agency" modelled on the Arpa programme in the US.
The Chancellor promised £27bn in road improvements, "the biggest ever investment in strategic roads and motorways" and said it would support the development of improved rail links between Manchester and Leeds to help boost the North's economy and increase the roll out of improved broadband nationally.
There will also be a £240m fund for new city and growth deals which could benefit areas such as Preston.
A "plastics packaging tax" charging manufactures and importers £200 per tonne on packaging made of less than 30 per cent of recycled plastic will be introduced in April 2022.
The Treasury will make £120m available immediately to repair defences damaged in the winter floods and the Government will double investment to £5.2bn flood defences over six years.
Mr Sunak said more than £600bn would be spent investing in future prosperity over the next five years, taking net public investment to the highest levels in real terms since 1955.
He announced that the so-called tampon tax will be abolished, VAT on women's sanitary products, and VAT on books, newspapers, magazines and academic journals will be scrapped from December 1.
And two and a half years on from the Grenfell fire tragedy, a £1bn building safety fund will be set up to ensure all unsafe combustible cladding is removed from buildings above 59ft (18m) tall.
Responding to the Budget statement, Labour leader Jeremy Corbyn welcomed the steps being taken to reduce the economic impact from coronavirus but said said the UK was going into the crisis with public services "on their knees" and an economy that was "flat-lining".
He said: "Today's Budget was billed as a turning point, a chance to deliver, in particular on the promises made to working-class communities during the general election. But it doesn't come close.
"The Government's boast of the biggest investment since the 1950s is frankly a sleight of hand. It's in fact only the biggest since they began their slash and burn assault on our services, economic infrastructure and living standards in 2010."