Describing his own experience as "pretty nasty", he told Good Morning Britain: "I had two days or so when it was like just razors in your throat, a very, very sore throat. I couldn't eat and I couldn't drink.
"The worst bit was on the way down, worrying how bad it would get because we've all seen how bad it can get and it seems to be indiscriminate."
He said he had also suffered a "bit of a cough" and lost half a stone in weight.
Mr Hancock came out of self-isolation yesterday but the prime minister is thought to still be self-isolating as he is still suffering from mild symptoms.
The Government has been criticised for not carrying out enough coronavirus testing, but Mr Hancock said he was committed to increasing testing capacity to 250,000 a day.
Currently, the number of tests being carried out each day in the UK is around 10,000.
Matt Hancock told ITV News Science Editor Tom Clarke it was "unfair" to say there had been a shift in opinion as to whether testing was critical to the UK's response to the coronavirus.
"I think that's a bit unfair on the team who have been ramping up to 10,000 tests a day. I set them that goal and they met it, to get to 10,000 by the end of March.
"After all, just a month ago, we had just under 2,000 tests a day and we were one of the first countries in the world to develop a test at all.
"And now we have the new goal, both for my team and the whole life sciences sector, to get to 100,000 tests a day by the end of the month."
Speaking on BBC Radio 4's Today programme, Mr Hancock said it is unclear whether he is now immune to Covid-19.
"I took advice on that and the advice is it's highly likely that I am now immune, or have a very high level of immunity," he said.
"But it's not certain."
Coronavirus: Everything you need to know: