Gilmour's positive result will force Clarke to rethink his starting line-up after the 20-year-old earned UEFA's man of the match award on his first international start during Friday's goalless draw with England.
The blow sparked fears that the Scotland squad might be decimated ahead of the Hampden clash with Croatia on Tuesday, which Scotland must win to retain hopes of progress.
But the only team-mates of Gilmour's who have been affected are his Chelsea colleagues Ben Chilwell and Mason Mount.
The midfielder was pictured embracing the two England players after the Wembley clash and the pair are isolating as a precaution pending further discussions with Public Health England (PHE).
The remaining 25 members of the Scotland squad all trained on Monday and showed negative lateral flow tests afterwards, following PCR tests.
After the squad flew to Glasgow in two planes Clarke claimed Gilmour’s 10 day self-isolation had caused "just a little bit" of disruption.
He added: "Obviously training was a little bit disrupted but the bulk of the work has been done.
"You saw for yourself the team know exactly what they are doing when they get on the pitch. The team has been organised, they know what they have to do, and that will stand us in good stead.
"The only spanner it throws into the works is that Billy would have started the game and now he won't, so it's a chance for someone else to come into the team and make themselves a national hero."
On Gilmour, manager Clarke said: "He's upset, as you would expect. He has no symptoms, so hopefully his health will hold up and he will get back to playing as quickly as possible."
When quizzed about the close contacts situation and how Gilmour might have contracted the virus, Clarke said: "It's not my department. My department is getting the team ready for an absolutely massive game against Croatia and that's what I have been concentrating on.
"The medical team I have got around me are good people and they deal with that side of the issue."