Omid Scobie accused royals of wasting an opportunity to present 'strong visual'.
Queen, 94, and Prince William, 38, both attended engagement without masks.
Everyone at engagement at Porton Down laboratory tested negative for Covid-19.
Many Twitter users felt Queen and Prince William were setting a 'bad example'.
Piers Morgan blasted the Queen and Prince William for appearing in public without wearing face masks today, calling it 'not a smart move by the Royal Family'.
Royal author Omid Scobie also suggested it was a wasted opportunity to present a 'strong visual' amid the country's ongoing fight against coronavirus.
The 94-year-old monarch, who falls into the 'at risk' age bracket for Covid-19, was joined by her grandson at the Defence Science and Technology Laboratory (Dstl) at Porton Down near Salisbury for her first public engagement since lockdown.
The duo met scientists who worked in the aftermath of the 2018 Novichok attack, and are currently supporting the UK's response to the coronavirus outbreak.
But while the pair maintained strict social distancing and arrived separately by helicopter and car, neither opted to wear face coverings - with all 48 people due to come into close contact with the royals tested for Covid-19 by Dstl beforehand.
In response to a tweet from Kensington Palace about the event, GMB host Piers tweeted: 'Why no masks or social distancing? Sorry, but this is not a smart move by the Royal Family as the virus rages and the country heads into another lockdown.'
Mr Scobie, who wrote the controversial biography Finding Freedom which raised eyebrows for its gushing praise and intimate knowledge of Prince Harry and Meghan Markle, tweeted this afternoon: 'No masks for anyone at today’s engagement, but Buckingham Palace confirm that the Queen consulted her own doctors and all staff at @dstlmod tested negative before the visit.'
He then followed up with a further tweet, writing: 'My two cents: While sensible and safe precautious were clearly made, I do worry that most people seeing the photos/videos won’t know the back story. As the majority of the UK enters tighter restrictions, seeing leaders in masks would have been a strong visual [sic].'
Both men's tweets sparked a passionate discussion, with a number of people accusing the monarch of sending a 'bad message' by failing to wear masks.
One Twitter user commented in response to Mr Scobie: 'Bad form, another one of the rules that apply for the plebs but not for the elite. Especially since Charles also flaunted them.'
Another wrote: 'Absolutely terrible message. We don’t even have to go through the incubation period issue. The optics are terrible as the country falls into a deeper and deeper mess, & public figures flouting basic mask wearing. Sigh.'
'Masks should be worn regardless of testing. This virus is still active,' exclaimed another.
Broadcaster Piers Morgan also criticised the monarch's decision not to wear a mask, saying it was 'not a smart move', while the pressure group Republic said the Queen should have set an example by wearing a face mask.
Others observed how it seemed to be different rules for the elite, after Donald Trump was photographed taking off his mask on his return to the White House after being treated for coronavirus.
However, some Twitter users felt Piers and Mr Scobie were making an issue out of nothing, with one tweeting: 'At first I thought it wrong that @RoyalFamily Queen and @KensingtonPalace were not wearing facemasks however the reality is that wearing masks is not law, they all tested negative and are all socially distanced. Ppl should not be trying to make a drama out of a non story.'
Another wrote: 'Bore off, everyone was tested prior and negative. There’s no problem here.'
And one added: 'Her Majesty the Queen would never have gone out if it was not safe to assume something else or to imply is a total sense of irresponsibility again I will say if it was not safe she would not be there.'
'Not worth two cents,' wrote another. 'She may have a medical exemption from wearing one. Ever thought about that?'
Today was the first time the Queen has ventured from a royal residence in seven months, outside of her household of reduced staff - dubbed HMS Bubble - to carry out her duties as head of state.
Royal author Robert Jobson told MailOnline the Queen chose not to wear a mask in a bid to send a message of calm and hope to the public.
The commentator said the royal had taken advice from her doctors who said it was safe to forego a mask, and ensured necessary measures were taken to protect everyone present from the risk of Covid.
Mr Jobson said: 'The Queen ensured there was a Royal safety bubble. She created a secure area where there was no danger to her or anyone else.
'She is sending a message of confidence to the people; she's going back to work, she'll go about her business in the usual way, but without taking chances. She is reassuring the public that things must go on as normal, wherever it is safe to do so.
'In a message of calm, she is saying you can make it work and things will get back to normal.'
Kensington Palace declined to comment as to whether the duke was also required to have a test in order to be able to accompany his grandmother.