The Chelsea midfielder impressed in his first Scotland start on Friday as he helped the team earn a goalless draw with England at Wembley.
That result left Steve Clarke’s side still in with a shot at reaching the knockout stages.
But Scotland have now received a major blow ahead of facing Zlatko Dalic’s team at Hampden, with the Scottish Football Association announcing the 20-year-old Champions League winner will have to quarantine for the next 10 days.
It is understood that no other players have been affected or identified as close-contacts, meaning all will be available for action on Tuesday.
“The Scottish FA can confirm that a member of the Scotland national team playing squad, Billy Gilmour, has tested positive for Covid-19,” the SFA said in a statement.
“Having liaised with Public Health England since the positive test was recorded, Billy will now self-isolate for 10 days and therefore miss tomorrow’s UEFA Euro 2020 Group D match against Croatia at Hampden.”
Having outshone a string of Premier League players in London on Friday night, Gilmour was expected to start again against Croatia, with the tantalising prospect of him going head-to-head with Real Madrid midfielder Luka Modric.
But Clarke will now need to rethink his plans. Manchester United midfielder Scott McTominay, who slotted back into a defensive role against England, is likely to be returned to his usual position protecting the back three.
Gilmour’s positive test is the second to hit the Scotland camp since the squad met up earlier this month.
Sheffield United midfielder John Fleck sat out both of the Scots’ warm-up fixtures against Holland and Luxembourg after contracting the virus.
Another six players missed the 2-2 draw with the Dutch as a precaution, although they were not formally designated close contacts of Fleck.