The video had already been viewed by 249,000 people and shared 1450 times two hours after it was uploaded this morning.
Harry's visit to the hospital was announced on the royal family's Facebook page 10 minutes before he was due to take the test.
He was doing it to "show how easy it is to get tested for HIV", the post said.
Kensington Palace said: "Until everyone feels relaxed about taking HIV tests - whether from higher-risk groups or not - then tackling the stigma and fear surrounding this simple test will continue to allow the virus to win, Harry believes."
Last month, when introducing Coldplay to sing at a concert hosted by his charity Sentebale, which helps orphans in Lesotho with HIV, Harry said: "HIV is a virus that thrives off silence and feeds on stigma."
At the beginning of the test, the healthcare worker doing the test, specialist psychotherapist Robert Palmer, explains the test is instant, taking around one minute for the result to come in.
"We call it either a reactive or non-reactive results,' he tells the Prince.
'If it was reactive it would be sent to the lab to confirm the result."
Psychotherapist Robert Palmer prepares to give Prince Harry the test. Photo / Getty Images
Harry admits he is nervous.
He said: "I'm not from this part of London. Even being the person I am and knowing the type of people I'm around, I'm still nervous, which is interesting."
Palmer says it is not surprising that he is nervous as there is a fear in "not knowing", but says it is his job to reassure anyone coming in for a test.
After Harry washes his hands, his finger is pricked and the swab is put into a special machine.
A minute later, it is revealed his test is negative.
"It's amazing how quick it is -- some people wait months for a blood test result,' he said.
Had the result been positive, Palmer explains, they would have a conversation about it and then Harry would have been sent for a blood test to confirm the diagnosis.
Palmer reiterated that many people taking daily medication to manage their HIV lead "long, full lives", have a partner and a healthy sex life.
Harry added: "Gay, straight, black, white, ginger, whatever - why wouldn't you just have a test?
"We all shouldn't be on the other side of the river saying "you should get the test", it should be normalised, everybody should get it."
Clinics in London and throughout the country offer the rapid result tests, Palmer explained.
In other places, people can expect the results within a day or up to a week later.
Last month, Harry announced he would follow in the footsteps of his mother Diana, Princess of Wales, and make the fight against HIV a major part of his public work.
Diana was the first member of the royal family to have contact with a person suffering from HIV/Aids and was a vociferous supporter of many charities.
Harry's charity, Sentebale, already focuses on supporting HIV positive young people in the African nation of Lesotho but the prince now aims to spread the message to his generation that the fight against HIV has not yet been won, Kensington Palace has said.
He is set to speak at an international Aids conference in Durban, South Africa next Thursday.
He will meet leaders to discuss the topic, sharing a stage with co-founder of Sentebale Prince Seeiso and Sir Elton John, a leading Aids campaigner since the 1980s.
Ian Green, chief executive of Terrence Higgins Trust, said: "Prince Harry's decision to take an HIV test, live on social media, is a groundbreaking moment in the fight against HIV.
"Not only does it show His Royal Highness' genuine and personal commitment to tackling the HIV epidemic, it will amplify a message to millions all over the world: testing for HIV is easy, quick and nothing to be feared.
"We have a real opportunity to end HIV transmissions in the UK, but it starts with each person knowing their HIV status. Too many people are either put off testing by the stigma that still surrounds HIV, or simply do not think HIV is an issue anymore.
Green continued: "Today, Prince Harry has got people talking about HIV again and has normalised HIV testing to a global audience. In doing so, he could inspire a generation to take control of their sexual health.
"Thanks to treatment, testing for HIV could stop you from getting seriously ill, enable you to live a normal lifespan and prevent you from passing the virus on to anyone else.
"That's why it's so invaluable to have Prince Harry's support as we aim to bust stigma and end the HIV epidemic."
HIV is a virus which attacks the immune system and weakens the body's ability to fight diseases.
An estimated 103,700 people are living with HIV in the UK and 6,000 people are diagnosed every year. Of these, 17 per cent are undiagnosed and do not know about their HIV infection.
In the UK, 103,700 people were living with the virus in 2014, yet it is thought one in six people remain undiagnosed.
And 40 per cent of newly diagnosed in 2014 were diagnosed late, when the virus has done a lot of damage and when HIV drugs may not work as well.
In the US, it is estimated there were 1.2 million people aged 13 or over living with HIV, including 156,300 who had not been diagnosed, according to the Centres for Disease Control and Prevention.
