Steve Clarke’s side are due to make the short trip to the Algarve to take on the Dutch on Wednesday June 2 before travelling to face Luxembourg at the weekend.
The former Rangers youngster won’t make the trip to Portugal and will almost certainly miss the Luxembourg match too.
No other players are understood to be affected, with the remaining squad members retested as a precaution.
Fleck is now self-isolating as per Spanish guidelines.
A statement read: “The Scottish FA can confirm that John Fleck has tested positive for COVID-19 at the Scotland National Team basecamp in La Finca.
“As a result, he will self-isolate as per Spanish Government guidelines and therefore not fly to Portugal for tomorrow’s match against Netherlands.
“The rest of the squad was retested for COVID-19 and returned negative results today.”
Clarke discusses Fleck result
Scotland manager Steve Clarke gave an update on the 29-year-old in a press conference.
"John's fine,” he said. “No symptoms. 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."
Clarke is eager for Fleck’s positive result not to disrupt the team’s preparation as they gear up to face the Netherlands and Luxembourg – and continue getting ready for the country’s first appearance at a major tournament since 1998.
The squad has been put through its paces at a training camp in Spain and the head coach has been pleased with the hard work put in so far.
He added: "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 looking 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."