Thomas Tuchel's side host Croatia at Wembley on Thursday before playing world champions Spain in Madrid on Sunday.
Guehi had featured in England's last 15 matches, but the City centre-back will miss out due to a reported hip issue, giving Burn a chance to return to the squad for the first time since the World Cup in June and July.
The 34-year-old Burn missed the previous international break in September and October with an ankle injury.
"Dan Burn has been added to the England squad following the withdrawal of Marc Guehi through injury," the FA said on Monday.
"The Newcastle United defender, who has 11 caps, joined up with the rest of Thomas Tuchel's group at Tottenham Hotspur's training ground on Monday.
"Guehi was substituted at half-time of Manchester City's fixture at Nottingham Forest on Saturday and will now remain with his club."