Video report by ITV News Political Correspondent Shehab Khan
Speaking at the government's daily coronavirus briefing, Mr Sunak also said the prime minister has been sitting up in bed and engaging with his clinical team.
The Chancellor said Mr Johnson is receiving "excellent care", before adding: "The latest from the hospital is the Prime Minister remains in intensive care where his condition is improving.
"I can also tell you that he has been sitting up in bed and engaging positively with the clinical team.
"The Prime Minister is not only my colleague and my boss but also my friend, and my thoughts are with him and his family."
Mr Sunak added: "The news about the PM reminds us how indiscriminate this disease is. Nearly everyone will know someone who has been affected – friends, family, neighbours, colleagues.
"This is a terrible virus that respects no boundaries of status or geography or vocation."
Mr Sunak said all Britons are taking part in a "collective national effort" to protect vulnerable people and public services and to save lives.
Health Secretary Matt Hancock tweeted: "So good that the PM is sitting up and his condition is improving. He will fight through!"
The prime minister, who was admitted to London's St Thomas’ Hospital's intensive care unit (ICU) on Monday evening, is "clinically stable" and in "good spirits" a Downing Street spokesman said earlier.
The spokesman also confirmed Mr Johnson was no longer working, despite his desire to lead the country's response to coronavirus, even from hospital.
ITV News Political Correspondent Libby Wiener has the latest on how the government is functioning while the PM is in hospital:
Mr Johnson had on Monday been due to oversee a three-week review of the lockdown rules – brought in last month to curb the spread of the disease.
Downing Street said it will go ahead as planned, but that the public needed to “stick with it” at a “critical time” in the epidemic.
The Prime Minister’s official spokesman said the review would take place “on or around” the three-week mark on Monday.
However, with the number of cases continuing to rise, Health Minister Edward Argar on Wednesday morning made clear now is not the time to start easing the restrictions.
“We’re not there yet and I don’t exactly know when we will be. The scientists will tell us that they are constantly modelling the data and they’re constantly looking at those stats," he told the BBC.
The prime minister's spokesman told reporters both the chief medical officer and chief scientific advisor had both made clear it's too early to say when the coronavirus peak would be reached, and it would be safe to ease the restrictions.
Tuesday night was Mr Johnson's second overnight stay in intensive care and his third night in hospital after his Covid-19 symptoms worsened.
He revealed he had coronavirus on Friday March 27 after experiencing mild symptoms the previous night.
He posted an update on Twitter saying his symptoms, which included a cough and fever, were "mild", adding how he planned to continue leading government, but from isolation in Number 11.
A week later, Matt Hancock, who was diagnosed with coronavirus around the same time as the PM, returned to work after a period of self isolation.
Asked if anyone has been in contact with the PM, the spokesman said: “The PM is not working, he’s in intensive care, he has the ability to contact those that he needs to, he’s following the advice of his doctors at all times.
“We are hugely grateful for the messages of support that the Prime Minister has received.
“I think the public response to coronavirus throughout has been fantastic and that has been best exemplified by the applause they’ve been giving to NHS staff every week.”
It followed a similar warning on Tuesday from Foreign Secretary Dominic Raab – who is deputising for Mr Johnson in his absence – who said ministers first need to see evidence that the measures are working.
Coronavirus: Everything you need to know