The Austria international made his first appearance of the season on Saturday, with new manager Gordon Strachan naming him at left-back for the visit of Plymouth, but his comeback was halted early in the second half following a clash of heads with Argyle defender Shane Lowry.
Pogatetz underwent surgery on Sunday and a Boro spokesman told the Evening Gazette: "Emanuel has fractured his left cheekbone."
He added: "It's a recurrence of the injury he suffered playing against Basel in the UEFA Cup March 2006.
"He underwent surgery in James Cook Hospital on Sunday and the surgeon will review the operation within a week.
"Generally, the normal recovery time for this injury is six weeks, though he may be able to play sooner subject to medical clearance allowing him to wear a face mask."