Derby will check on Russell Anderson, who was forced off after 35 minutes against Birmingham on Saturday with a groin problem.
"It is ironic because Russell is one of the few players who did every single day in pre-season and he has been feeling good," said Rams boss Nigel Clough.
"He did the same on the opening day at Leeds 12 months ago and he is devastated. We will see how it is. He will have a scan and we will take it from there."
Anderson joins fellow central defenders Shaun Barker, Jake Buxton and Dean Leacock on the sidelines.
Jamie Ward and Jeff Hendrick will miss the tie after receiving international call-ups. Striker Ward is in the Northern Ireland squad for their Euro 2012 qualifier against the Faroe Islands on Wednesday, while midfielder Hendrick has been named in the Republic of Ireland Under-21 squad to play Austria on Tuesday.
Forward Nathan Tyson will be missing until next month with the groin injury that ruled him out against Birmingham.
Marvin Morgan will be assessed by Shrewsbury.
The striker put in a solid debut shift in Saturday's opening-day 1-1 draw against Plymouth but was forced off in the 88th minute having gone down off the ball, with the summer signing having also taken a knock earlier in the encounter.
Left-back Joe Jacobson serves the second game of the three-match ban he picked up while playing for Accrington last season, while striker Tom Bradshaw continues to receive treatment on the cruciate knee ligament damage he sustained during pre-season.
Shrews saw off Charlton in the first round of the cup competition last year having taken Ipswich all the way to penalties the previous season, and manager Graham Turner is looking to give the Rams a run for their money at Pride Park.
He told Town's official website: "They beat Birmingham on Saturday so it should be a tough test for us on Tuesday night. The pressure might seem to be off but that's our place in the Carling Cup and we want to be in the next round.
"We've proved against decent sides in the past that we are capable of causing upsets. We can go there and play with an amount of freedom but will have to be at our best both individually and collectively."