Carter, a four-year veteran out of Georgia, did not practice with the team Wednesday.
There was no immediate word as to why the Cowboys planned to cut Carter.
Carter, 26, started all 16 games last season, when the Cowboys went 10-6 and got back in the playoffs in head coach Bill Parcells' first year with the club.
Just last week Carter said he expected to be Dallas' starter when the 2004 season opened.
"I wouldn't say it's an open competition," Carter said last Saturday, after the team's first workout. "I'm clearly the starter right now. ... The team knows who their starter is. I'm going to stand firm on that, and I'm going to be their leader."
Indeed, Carter took snaps with the first team when camp opened, and Parcells at first acknowledged that his '03 starter had the advantage.
"He has a leg up on pretty much everybody because he was the guy that played the best and started last year," Parcells told The Associated Press last week. "Obviously I have that in mind. He is in a good position to be improved. And that is what I'm looking for."
However, Parcells has also maintained that no one -- not the incumbent, not a former star like Vinny Testaverde -- is a given in the position. Former New York Yankees player Drew Henson is also competing for the starting spot.
After last season, Parcells gave Carter a list of some things he wanted the quarterback to do during the offseason. Among them was to add muscle, work on certain mechanics and footwork and get better throwing on the run to cut down his high interception total.
Carter added four pounds of muscle, getting to 219 pounds. He's a long way from the pudgy-looking 223-pounder he was when the coach arrived.
Despite the obvious changes, however, it would take time to see if Carter improved on the field the way Parcells expected.
In his first season as the full-time starter -- after splitting the first two seasons with Chad Hutchinson -- Carter threw for 3,302 yards, but had 21 interceptions and 17 touchdowns. He was intercepted at least twice six times.
Thirteen of those interceptions came when he got outside the pocket after a play had broken down.
Carter was a chosen by Dallas in the second round of the 2001 draft.
Information from The Associated Press was used in this report.