The youth team will host Oxford United in the FA Youth Cup third round.
The Clarets knew their opponents would be either Oxford United or Barnet after the third round draw.
And United edged out the Bees in a 1-0 win on Tuesday night to secure their trip to Burnley, with Striker Slavi Spasov scoring the only goal of the game.
Oxford are currently top of the Youth Alliance League and have lost just twice all season.
Date and venue to be announced in due course.