Burn, on loan from Fulham, missed Saturday's 4-1 win over Oldham after picking up his fifth yellow card of the season against Walsall.
But Johnson will be without midfielder Korey Smith who has returned to parent club Norwich. The Glovers are currently in talks with the Premier League outfit about bringing Smith back to the club but the move would not take place in time for the Boxing Day clash.
Full-back Joe Edwards, who has been with the club since September from Bristol City, has returned to his parent club after playing the final game of his loan spell on Saturday.
Johnson will assess midfielder Sam Foley after he limped off after 27 minutes during the 4-1 victory.