The former They Think It's All Over panellist said whatever happened to the Chief Medical Officer 'was not enough'.
His comments came after the epidemiologist was jumped on by yobs in St James's Park in central London on Sunday night.
Footage emerged on Monday of them following Prof Whitty and putting him in a headlock as he walked home.
Mr Hurst, 57, who says he is a 'proud covidiot', today launched his tirade against the top scientist on social media.
But his posts were quickly seized on and reported to Twitter and the police for 'inciting hatred'.
Mr Hurst told his 18,000 followers on Tuesday morning: 'Whatever has happened to Chris Whitty is not enough.'
He later put: 'I'm not putting any caveats into the Chris Whitty story. Fk him and his #FullPay, care home murdering scummy pals.'
And he added: 'If there was no video footage of Chris Whitty we would have been told he was beaten up.'
Prof Whitty was followed and put in a headlock by two thugs as he walked through St James's Park on Sunday night.
He was also targeted by lockdown sceptics who demonstrated outside his London flat on Saturday afternoon.
The first attack was widely condemned by politicians and public figures, with Boris Johnson branding it 'despicable harassment'.
Mr Hurst faced a swift backlash to his tweets, with anti-hate firms and social media users slamming him for inciting hate against Prof Whitty.
Tell Mama UK, which records anti-Muslim incidents, said: 'We have flagged this abhorrent tweet from Lee Hurst regarding Professor Chris Whitty and encourage others to do the same.'
Barrister Rupert Myers said: 'Lee Hurst there, inciting violence.'
Former rugby player Brian Moore put: 'Whitty's father was dragged out of his car and murdered by terrorists in Athens. Lee Hurst is ignorant and a coward.'
Other social media users also joined the pile on, questioning Mr Hurst's right to quibble with an expert.
One wrote on Twitter: 'You seem to be inciting violence against a scientist. Reported.'
Another put: 'You should be grateful to him. Thanks to the 30 person limit, your tour can officially be classed as a sell-out.'
And one added: 'I'd rather listen to someone who has five medical degrees, still does his rounds and worked on Christmas Day on a virus that he will slightly know more about than a washed up 'comic'. You've never had an edge.'
The Prime Minister condemned the 'thugs' who accosted England's chief medical officer.
Mr Johnson hit out after the video posted online appeared to show Prof Whitty being harassed in the central London park.
He said: 'I'm shocked at seeing the despicable harassment of chief medical officer Chris Whitty.
'I condemn the behaviour of these thugs. Our hard-working public servants should not have to face this kind of intimidation on our streets and we will not tolerate it.'
The Metropolitan Police are investigating after the footage, lasting around 20 seconds and apparently taken in St James's Park, was shared on social media.
It shows two grinning men grabbing Prof Whitty as they shout 'Oi oi' and say 'One photo please?'
As Prof Whitty tries to walk away, the men grab him again.
With a line of police vans visible in the background, a voice is heard saying 'leave the gentleman alone' before the clip ends.
This is the moment two thugs appear to grab government advisor Professor Chris Whitty and put him in a headlock as they harass him in a park as he grapples with them to get away
Chief Medical Officer for England Prof Chris Whitty is seen walking past the Department of Health and Social Care in London on Monday afternoon
Home Secretary Priti Patel said she was 'just horrified' by the incident and that officials are looking at support available to Prof Whitty.
Asked if he needs security measures, she told Times Radio: 'I can't speak about that but it's important that we make sure that Chris is given the right kind of support.
'It's terrible to see such an important public figure, someone that day in, day out, has been serving our country in the way in which he has to keep us safe, being subject to just appalling abuse.'
Health Secretary Sajid Javid also condemned the behaviour.
'I've seen the video of the CMO being harassed,' he said. 'It's appalling and totally unacceptable. The CMO works tirelessly on behalf of the country.
'We will not tolerate this sort of behaviour towards our public servants. The men behaving in this disgraceful way should be ashamed.'
The Met tweeted: 'We are aware of a video being shared online showing an incident in St James's Park. Officers spoke to all those involved at the time and their details were taken.
'We are in contact with the victim and the circumstances continue to be investigated.'
A number of other MPs were swift to condemn those involved in the latest incident.
During the terrifying video, Prof Whitty looks concerned as he tries to escape their grasp while the thugs appear to laugh off his attempts
Politicians and public figures have slammed the attackers after the video was viewed more than half a million times online
Labour leader Sir Keir Starmer said: 'This is disgusting behaviour. Chris Whitty is a dedicated public servant who has worked tirelessly to help get us through this crisis.
'The police are right to investigate this harassment.'
Vaccines minister Nadhim Zahawi tweeted: 'This is disgusting and these thugs must be found and charged. Zero tolerance for harassing a public servant.'
Schools minister Nick Gibb described those responsible as 'yobbos', telling LBC that Prof Whitty has been a 'first-class chief medical officer throughout the pandemic, providing very high-quality advice to Government, providing very calm advice to the public in those press conferences'.
Labour MP Jess Phillips said Prof Whitty had been made to feel 'awful and uncomfortable' and issued a reminder that public figures 'are human beings'.
'Even if you perceive it as non violent it is clear that he felt awful and uncomfortable and resisted,' Ms Phillips tweeted.
'Public figures are not dolls, they are human beings, it is stunning how easily this is forgotten.'
It is not the first time Prof Whitty has been forced to endure public harassment.
Earlier this month, he was confronted in a street in Oxford by a man accusing him of lying to the public about coronavirus, while in February a man accosted the chief medical officer outside Westminster.
The incidents were filmed on mobile phones.
Prof Whitty brushed off the February incident, addressing it at a Downing Street press conference shortly afterwards.
He told viewers: 'In terms of being harangued ... the odd young lad showing off occasionally happens.
'I didn't think anything of it, frankly. I was very surprised it was picked up by the media at all, as anything of any importance.'
He added that he was sure the person involved would 'become a model citizen in due course', hoping they could be more like much-admired NHS charity fundraiser the late Captain Sir Tom Moore.
