The Scottish FA confirmed the change on Sunday, the day Scotland's party flew to Florida to begin their World Cup preparations. Fletcher, 19, is the son of former Scotland and Manchester United midfielder Darren Fletcher and made his senior international debut as a half-time substitute in the Curaçao match.
Head coach Steve Clarke had mentioned Rangers midfielder Connor Barron, Sparta Prague's Andy Irving and Udinese's Lennon Miller as standby options, but chose Fletcher after his immediate impact at Hampden left both players and staff impressed.
"Everybody was impressed — the players, the coaching staff," Clarke told BBC Scotland. "I actually thought about putting him on as Billy came off but I just thought I'd have a little look, see how the game panned out before introducing him at half-time."
Kenny McLean, the Norwich City midfielder who played alongside Tyler's father at the start of his international career, had singled the teenager out from his first training session.
"In my first session with Scotland, Darren stood out a mile. Fortunately for us, his son is pretty similar. I said to the lads after his first session, I could see something special in him."
Fletcher has made two first-team appearances for Manchester United this season, meaning his Scotland debut came before he had accumulated significant senior minutes for his club. His twin brother Jack has chosen to represent England at youth level.
Clarke was devastated for Gilmour.
"The timing of this injury is so, so cruel and we all feel for him. He knows what we all think of him as a footballer and a person, and while no words will give him any comfort, I am certain Billy will have many major tournaments ahead of him in the future."
Gilmour's Napoli teammate Scott McTominay wrote on Instagram: "Absolutely devastated for you brother. Football is a cruel game and you don't deserve this, keep your head up. The players, staff and country love you."
Scotland will face Haiti, Morocco and Brazil in Group C. They play a final warmup match against Bolivia in New Jersey on June 6 before the tournament begins on June 11.