Sunak was speaking to the Lords' economic affairs committee and added that the economy is likely to see a huge downturn.
The number of people claiming unemployment benefits soared to 2.1 million in April, the first full month of the strict social distancing measures that shut down most businesses.
"Obviously the impact will be severe", he said.
About 8m jobs have been protectedthrough the government's furlough scheme. We are getting data from around Europe and around the world as countries are progressively easing and lifting restrictions. But with the gradual reopening of the economy as lockdown controls are lifted over the coming months, the chancellor is preparing to scale back the support from the current level of 80% of workers' wages and pass some of the £14bn-a-month cost of the scheme to employers.
The emergency financial support unleashed by the Treasury, with a rapidly rising price tag worth tens of billions of pounds every month, is created to minimise the lasting damage to the economy by helping companies to stay afloat and by keeping people in their jobs.
It is not obvious that there will be an immediate bounce back. "We are likely to face a severe recession, the likes of which we haven't seen, and of course that will have an impact on employment", said Sunak.
'Those things will all take time. "So I think, in all cases, it will take a little bit of time for things to get back to normal, even once we've re-opened now closed sectors", he said.
Jonathan Athow, deputy national statistician for economic statistics at the ONS, said: "While only covering the first weeks of restrictions, our figures show Covid-19 is having a major impact on the labour market". The Office of Budget Responsibility has previously suggested unemployment could reach "double digits" in the wake of the pandemic.
The UK is facing a severe recession "the likes of which we have not seen" due to the Covid-19 crisis, Rishi Sunak warned, as the number of people claiming unemployment benefits soared by almost 70 per cent.
On how the country might recover once the pandemic is over, Sunak explained: "We all would hope that it is as swift and strong as it can be".
"I think when it comes to the hospitality sector, I think we do need to look at it very carefully", he said.
The Treasury revealed yesterday that more than £11.1bn had been claimed so far through the coronavirus job retention initiative.