The Jaguars placed Kirk (collarbone) on injured reserve Saturday.
Kirk's left arm was in a sling after Sunday's 30-27 loss to the Packers, Michael DiRocco of ESPN.com reports.
Kirk suffered an injury to his left shoulder with 13:24 remaining in the fourth quarter of Sunday's game against the Packers and has been ruled out for the remainder of the contest, John Oehser of the Jaguars' official site reports. He recorded two catches for 59 yards on five targets prior to departing.
Kirk brought in one of three targets for 24 yards in the Jaguars' 32-16 win over the Patriots on Sunday in London.
Kirk brought in three of six targets for 39 yards in the Jaguars' 35-16 loss to the Bears on Sunday in London.
Kirk brought in all four targets for 88 yards in the Jaguars' 37-34 win over the Colts on Sunday.
Kirk caught seven of 12 targets for 61 yards and a touchdown in Sunday's 24-20 loss to the Texans.
Kirk brought in one of four targets for 30 yards in the Jaguars' 20-17 loss to the Dolphins on Sunday.
Kirk (calf) was a full participant in practice Wednesday.
Coach Doug Pederson said Monday that Kirk (calf) will resume practicing this week, John Shipley of SI.com reports.