Hearts captain Berra has been capped up to B squad level and was named in former manager Alex McLeish's full squad to face South Africa at Pittodrie in August.
However, on that occasion the defender was forced to withdraw through injury.
Hibernian's Fletcher has featured regularly in the Under-20 and Under-21 sides and will celebrate his 21st birthday on the day of the game.
The striker has been in fine form recently and scored his 14th goal of the season in the weekend win over Kilmarnock.
"Steven is one of the leading goalscorers in the SPL - he has got talent," said Burley.
"He is a player I have admired for a long time.
"With his quality, he is another youngster who deserves his opportunity in the full squad."
Scotland squad: Goalkeepers Craig Gordon (Sunderland) David Marshall (Norwich City) Allan McGregor (Rangers)
Defenders Graham Alexander (Burnley) Russell Anderson (Sunderland) Christophe Berra (Heart of Midlothian) Gary Caldwell (Celtic) Christian Dailly (Rangers) Alan Hutton (Tottenham Hotspur) James McEveley (Derby County) Stephen McManus (Celtic) Gary Naysmith (Sheffield United)
Midfielders Scott Brown (Celtic) Barry Ferguson (Rangers) Darren Fletcher (Manchester United) Paul Hartley (Celtic) Lee McCulloch (Rangers) Stephen Pearson (Derby County) Barry Robson (Celtic) Gary Teale (Derby County)
Forwards Kris Boyd (Rangers) Steven Fletcher (Hibernian) James McFadden (Birmingham City) Shaun Maloney (Aston Villa) Kenny Miller (Derby County) Garry O'Connor (Birmingham City)
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