Mincey's latest setback came Wednesday, the same day he was promoted to a starter over former first-round draft pick Derrick Harvey. Mincey calls it "Jeremy Mincey luck."
Mincey broke the same hand last year. He broke his left wrist in 2007 and again in 2008. He calls the injuries "freak things," adding that doctors tell him he has really strong bones.
Harvey, the eighth overall pick in 2008, has just six sacks in 39 career games.
"It's part of the business," said Harvey, a former Florida standout who was the defensive MVP of the 2006 Bowl Championship Series title game. "Obviously, I wasn't doing what I was supposed to do, and I'm having to step my game up and do things differently than I did in the past."
Todd Bouman, who started in Garrard's place last week, is questionable with a right finger injury, meaning Trent Edwards -- listed as probable with a right thumb injury -- is likely to backup Garrard.
For Dallas, guards Montrae Holland (groin) and Kyle Kosier (ankle) have both been ruled out, meaning rookie Phil Costa will start at left guard.
Starting CB Terrence Newman (ribs) is questionable, while wide receiver Dez Bryant (ankle) and linebacker Bradies James (knee) are both probable.
The Associated Press contributed to this report.