Holgorsen said on his statewide radio show that the redshirt freshman Childress has a torn pectoral muscle and didn't practice this week.
Trickett, a junior, will be the third starter this season for the Mountaineers (2-2, 0-1 Big 12) when they play the Cowboys (3-0, 0-0) on Saturday.
Trickett transferred from Florida State after graduating in the spring. He played two series in the season opener against William & Mary but didn't complete a pass and failed to get a first down.
Trickett played eight games for the Seminoles last season as EJ Manuel's backup and went 22 of 34 for 272 yards. In 2011, he started games against Wake Forest and Clemson. He passed for 336 yards and three touchdowns at Clemson.
Trickett's father, Rick, spent six seasons as offensive line coach at West Virginia before leaving for the same job at Florida State in 2007.