The young goalkeeper landed awkwardly, twisted his ankle and had to come off a few minutes from time in Wednesday night's win against Wimbledon at Milton Keynes.
It's a blow for 'Burchy' as he's been Kasey Keller's deputy on the bench for most of the season.
As a result, the club has recalled Lars Hirschfeld from his loan spell at Gillingham and he will be on the bench against Newcastle United on Sunday.
Acting boss David Pleat revealed: "Robert went over on his ankle on Wednesday and could be out for five or six weeks, so we're a goalkeeper light.
"We've recalled Lars Hirschfeld from a loan spell at Gillingham where he's had two good games, a win and a draw in a side that's fighting for its life. He will be on the bench on Sunday."
Robert Burch is expected to be out for over a month after picking up an ankle injury on reserve duty.