He underwent arthroscopic knee surgery Aug. 1 and has not healed fully.
The 33-year-old Glenn, an 11-year NFL veteran, missed the preseason after having the knee scoped to remove a cyst from the back of his right kneecap.
Team owner Jerry Jones said on the Cowboys' Web site the problem will force Glenn to miss two weeks and possibly more.
"With the offense (offensive coordinator) Jason (Garrett) has, it will give us the flexibility with the players we’ve got to help us overcome this,” Jones said. “We'll adjust.”
Last season, the first-round draft pick of New England in 1996 out of Ohio State scored six touchdowns on 70 receptions for 1,047 yards.
He will be replaced in the lineup by Patrick Crayton.