Brinkley suffered an ACL sprain during Minnesota's loss to the Chicago Bears in Week 12, though the linebacker vows to play in Week 13.
Percy Harvin (ankle), Phil Loadholt (knee), Harrison Smith (concussion) and Antoine Winfield (knee) were also listed as limited in practice.
Tight end Kyle Rudolph did not practice. Rudolph suffered two injuries on Sunday: a concussion and a strained shoulder. The two injuries occurred on the same play.
Jared Allen, Letroy Guion, Adrian Peterson and Chris Kluwe were also listed on the injury report, but were full participants in practice.
A win over the Packers on Sunday would move the Vikings into second place in the NFC North, as the two teams would be even with a 7-5 record -- but Minnesota would own the tiebreaker.