Jones was ruled out with a torn calf, while Leigh Halfpenny will miss all four games with ankle ligament damage.
Rees, 29, will take the armband on the occasion of his 40th cap and despite leading a depleted side, Jenkins believes he will shine.
"We used to be room-mates at Pontypridd and the Celtic Warriors," said Jenkins.
"I think he's developed into an awesome player. He's been outstanding for the Scarlets, Wales and the Lions over the last few years.
"It's a fantastic achievement for him and his family to be chosen as skipper and I think it's fully deserved.
"He's a leader, but it's basically what he does on the pitch. If he plays like he normally does, we will be fine."