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Head coach Johan Ackermann confirmed the news at Thursday’s team announcement ahead of Saturday’s United Rugby Championship clash against Ulster at Loftus Versfeld.
Papier, the reigning SA URC Player of the Year, was hurt after coming off the bench in the Bulls’ 56-20 Champions Cup win over Stade Français in Pretoria last Saturday.
His absence leaves Paul de Wet and Zak Burger as the scrumhalf options in the match 23.
De Wet keeps the No 9 jersey and again partners flyhalf Handré Pollard.
Ackermann has made wholesale changes to the forward pack for Saturday, but has kept his starting backline unchanged.
Regular captain Marcell Coetzee returns in place of Elrigh Louw, who shifts from openside flank into the number eight jersey.
The front row sees a complete overhaul from last week’s win over Stade Français, with Gerhard Steenekamp, Johan Grobbelaar, and Francois Klopper all promoted from the bench to start, while Alu Tshakweni, Jan-Hendrik Wessels and Khutha Mchunu make way.
Steenekamp and Grobbelaar slot in at loosehead and hooker respectively, with Klopper taking over at tighthead.
The second row also looks markedly different, with Ruan Vermaak and Reinhardt Ludwig handed starts in place of Cobus Wiese and JF van Heerden, neither of whom features in the match-day 23 this week.
Hanro Liebenberg comes in at openside flank, while Marco van Staden, who started at six against Stade Français, drops to the bench.
Coetzee moves into the six jersey and assumes leadership duties, with Louw’s shift to the back of the scrum pushing Cameron Hanekom, last week’s starting number eight, into a reserve role.
This weekend’s action kicks off when the Sharks and Cardiff face off in Wales on Friday, while Connacht will welcome Italian side Zebre to Ireland.
On Saturday, the Lions are away to Edinburgh in the Scottish capital, while the Stormers are at home against Wales’ Scarlets.
Edinburgh are currently on top of the log after three rounds, followed by Glasgow Warriors, the Bulls and the Stormers.
The Sharks are fifth and the Lions seventh.