Adam Rooney netted a hat-trick as the Dons began the defence of their trophy in style but Jack’s injury overshadowed the Pittodrie triumph.
Manager Derek McInnes said: “He is a real concern to us at the moment because it is the follow-through from a challenge and I think on the inside of his knee there is damage there but we’re unsure of the extent of that yet.
“If I sound subdued, it is because of that really and I’m delighted to get through and keep another clean sheet but obviously we’re hoping it is nothing too serious for wee Jacko.”
Rangers joined the Dons in the last eight after coming from behind to beat Falkirk 3-1 and bounce back from their weekend draw with Alloa.
Rory Low netted the opener but an Owain Tudur Jones own goal soon levelled and second-half goals from Dean Shiels and Ian Black won it.
Gers left-back Stevie Smith said: “We knew they were going to come out of the blocks quickly and they did that.
“They got the opening goal but we showed good character to get back into the game and to go on and win it.
“After the weekend the manager wanted a reaction and going a goal down wasn’t the reaction he wanted.
“But we got the equaliser quickly after that and I think we deserved the win in the end.”
Partick Thistle manager Alan Archibald believes the competition is wide open after his side beat St Mirren 1-0 thanks to Nathan Eccleston’s extra-time tap-in.
“In the Premiership now, anyone can beat anybody on their day,” Archibald said.
“Obviously there are a couple of teams still in there outwith the Premiership, but I think, especially if you get a home tie, there is nothing to say you can’t continue in the cup.
“It’s given us great encouragement in the last few years with different teams getting to the final, and winning it.”
On-loan Dundee United striker Brian Graham scored his third goal for St Johnstone to earn them a 1-0 win at Kilmarnock.
Manager Tommy Wright said: “Brian has come in and you couldn’t ask for any more than three goals in three starts and one appearance off the bench and he will get better as he hasn’t played that many 90 minutes over the last calendar year.
“Once we play like we did at the start of the second half and get more supply into the box he is capable of scoring more goals.”
Hibernian are also in Wednesday night’s draw after Dominque Malonga’s headed double earned them a 2-0 win over Ross County in Dingwall.