Coach Gus Bradley says Mincey has a "head contusion," adding that the veteran is seeing a neurologist Friday for more testing.
Bradley says Mincey banged his head during drills Thursday.
Mincey has started the last 40 games for Jacksonville. He has 262 tackles and 18 sacks during his six-year NFL career.
The Jaguars also practiced without running back Justin Forsett (toe) and cornerback Lionel Smith (quadriceps). Forsett hyperextended a toe, an injury Bradley describes as "turf toe-type syndrome but not severe."