McClain left last Sunday's playoff game against the Detroit Lions due to concussion-like symptoms and did not play in the second half. Head coach Jason Garrett later said McClain was also dealing with an injured neck.
The 25-year-old is Dallas' second-leading tackler this season with 67. He also has a sack, two interceptions, three passes defended and one forced fumble.
Mincey also sustained a concussion during the Wild Card game and needed clearance to be allowed to play in Sunday's playoff game against the Green Bay Packers.
The 31-year-old pass rusher started all 16 games for Dallas in the regular season and led the team with six sacks. He also recorded 23 tackles and a forced fumble.
The Cowboys travel to Green Bay to take on the Packers at 1:05 p.m. ET on Sunday.
- Molly Geary