Turco, who is unbeaten in a franchise record-tying 14 consecutive decisions, sprained his ankle in Tuesday's 2-1 overtime win over the Carolina Hurricanes. He failed to come out of the locker room after the second period, and Ron Tugnutt came in to make just six saves for the victory.
Turco, 27, is in his first season as the No. 1 goalie after spending two seasons as a backup for Ed Belfour. He is 25-9-10 with a league-best 1.77 goals-against average, and also is second to Detroit's Manny Legace with a .931 save percentage.
The winning goaltender in the All-Star Game shootout, Turco is 10
4 in his last 14 decisions to equal the record Don Beaupre set with the Minnesota North Stars during the 1985-86 season.
Turco is listed as week-to-week as is Morrow, who has a chest contusion.
Morrow also was injured in Tuesday's game. He has 16 goals and 18 assists with a plus-22 rating in 55 games.
The Stars, who lead the Western Conference with 79 points, (33-11-12-1), are seven points ahead of St. Louis and Vancouver for the top spot in the West. They host Anaheim on Friday.
To replace Turco and Morrow, the Stars recalled goalie Corey Hirsch and center Steve Ott from Utah of the American Hockey League.
Hirsch was 11-11-2 with a 2.72 GAA and .971 at Utah, and Ott had nine goals and 11 assists.
Hirsch, 30, has not played in the NHL since the 2000-01 season, when he appeared in one game with the Washington Capitals. He is 34-44-14 with a 3.14 GAA in 106 career games.