Fletcher will wear the armband at Hampden on Saturday on his 40th international appearance. The honour continues a good month for Fletcher. The 24-year-old signed a three-year contract at Old Trafford last week.
Burley said: "Darren has been an outstanding player for Scotland for a number of years. "At the same time he has established himself as a regular player for one of the biggest clubs in the world.
"Since I took over, his attitude towards playing for his country has been outstanding. He is a player who is always desperate to represent Scotland. "It is a measure of his talent that at his relatively young age he has achieved so much for his club and will win his 40th cap for his country on Saturday.
"I know he will be very proud to lead the players out at Hampden on Saturday. He will do a great job for Scotland."