He added there would be no mandatory covid tests for the 6,000 daily ticket holders.
The Health Secretary told Parliament that the mitigation measures in place would limit the spread of the virus.
He warned the zone would be closed if ‘significant concerns’ arise.
The comment from the professor comes as the Daily Telegraph reported that Glasgow currently has the ‘softest entry rules’ for fans of the 11 host cities across Europe ahead of the Euros.
A guide published by Uefa shows that fans in Glasgow only need a ticket and a mask to gain entry while most other venues require fans to prove they have been vaccinated or recently tested negative.
It was confirmed on Wednesday that at Wembley – where Scotland will play against England on June 18 – fans will need to provide a negative lateral flow test result or proof of full vaccination.
Linda Bauld said that it is ‘too late’ to introduce mandatory covid testing to Glasgow the fan zone but said it should have been introduced by the government for the event.
She told the programme: “I think if it’s just people moving around outside and there’s distancing that’s maintained then that’s low risk but it’s all the things that come with a mass event.
"People taking public transport, using toilets and maybe other indoor spaces and then if the matches get underway and the results are good, people might lose some of their inhibitions and they might be embracing so that has risks.
"It’s definitely not without risks – it’s definitely less risky than a mass indoor event but it’s also controversial as when you contrast this with all the other things which are still restricted, it’s hard for some families, communities and sectors to understand the logic.”
Murdo Fraser, the Scottish Conservatives’ spokesperson for covid recovery said he believed it was “absolute nonsense” to allow the mass event to go ahead whilst not allowing parents to attend their children’s Sports Day.
On mandatory covid testing, Professor Bauld said it should have been introduced for those participating in the fan zone, however, commented that it is ‘too late now’ to do so.
Professor Bauld added: “It’s not the sort of thing you could do now, it requires a lot of organisation and set up.”
Wishing that all goes well in the fan zone, Professor Bauld urged those going to take up voluntary lateral flow tests available to everyone in the country.
She said: “Test yourselves the day before and ideally the morning before you go just to make sure you don’t have a positive result.
"Maintain distancing while you’re there, follow all the guidance – that’s the best that people can do for themselves and for their families.”