Sheffield United midfielder Fleck has returned a positive test for the virus after joining up with Clarke's squad in Spain for their pre-tournament training camp.
Fleck will now follow Spanish coronavirus rules and self-isolate at the Scots' training base in La Finca – meaning he will play no part as the team hop across the border to Portugal for their opening warm-up friendly against Holland at the Estadio Algarve on Wednesday night.
With the Scots due to kick-off their first major tournament in 23 years back home in Glasgow against the Czech Republic on June 14, this is the scenario Clarke has been dreading.
But the Scotland boss has been reassured by the Scottish Football Association's medical team that Fleck is likely to have arrived in camp already carrying coronavirus in his system.
And even though he flew out on the same flight from Glasgow Airport as the rest of the squad last Thursday, social distancing measures put in place on the plane have ensured the other 23 members of the team that have met up so far have returned a full sweep of negative results.
"John's fine," said Clarke. "No symptoms. Obviously he's got to isolate for a few days now but we'll keep an eye on him, we'll look after him as we do with everybody. Hopefully it stops there.
"Looking at the information we've got and relying on the doctors for the medical opinion we're 99 per cent sure that John brought it into the camp, it came with him.
"It's just one of those things with the state of the world at this moment with the pandemic.
"We just have to deal with it, as other countries might have to deal with it as well.
"John will be in isolation until he returns a couple of negative tests. I'm not quite sure what the guidelines are in Spain in terms of the number of days he will have to isolate for.
"But we'll be testing every day with John and waiting for him to return a few negative tests.
"For everyone else, it's just carry on as normal and continue the good work. The thing I don't want is for this isolated case to overshadow the good work that we've done.
"We've had good preparation. The training has been fantastic. The boys are in a great place and we're working forward to the game tomorrow night.
"We all want to avoid the virus as much as we can and that's certainly no different within the camp.
"We'll have to be reactive to certain situations but there's no point stressing about it.
"There are certain situations that you can't control. We can control the lads in training, preparation for the matches and hopefully a good performance tomorrow night against the Dutch."
Fleck will now be absent for the Holland clash along with Chelsea midfielder Billy Gilmour and Manchester United counterpart Scott McTominay following their involvement in last week's European finals.
But Clarke is hopeful he will have a full squad to chose from by the time they face Luxembourg on June 6 in what will be the team's final dress rehearsal before the finals start.
And he believes this week's friendlies are the perfect preparation as his side look to become the first Scottish team to make the knock-out stages at a major competition.
Clarke – whose side also face England and Croatia in Group D – said: "We wanted one game that would challenge us and certainly the Dutch game will do that. The Luxembourg game will challenge us in a different way.
"The way the Dutch play is not dissimilar to the way that certainly England play, and maybe a little bit like Croatia as pot one teams.
"It should be a good workout for us in terms of the friendly and a good workout for us in terms of the games coming up in the tournament.
"We're slowly, slowly getting towards where we want to be, which is the first game of the tournament. It's a process and we're working towards that.
"There's a good feeling in the camp. There's obviously a little bit of deflation when you get the news about John, everybody feels that a little bit.
"It's come early enough though, so it shouldn't affect our preparations too much."