The 25-year-old was booked for the fifth time this season during the Bluebirds' 1-0 victory over Leicester on Saturday and will serve a one-match ban.
Experienced defender Kevin McNaughton is expected to deputise at right-back in Connolly's absence.
Former Watford attacker Tommy Smith is edging closer to a return to action but manager Malky Mackay is unlikely to risk him at this stage.
Nicky Maynard is out for the rest of the campaign with a knee ligament injury but midfielder Kadeem Harris is close to making a comeback after sustaining an ankle problem.
The league leaders will be looking to return to winning ways at the Cardiff City Stadium after losing their first home match of the season against Peterborough last time out.
Meanwhile, Crystal Palace are without the suspended Damien Delaney for the trip to league leaders Cardiff.
The defender was dismissed after just 11 minutes of the Eagles' 1-1 draw with Huddersfield on Saturday and starts a three-match ban.
Danny Gabbidon could be handed his full debut in Delaney's absence following two substitute outings.
Midfielder Jonny Williams is looking to be involved after returning from a groin problem and is targeting a place on the bench.
Skipper Paddy McCarthy remains sidelined with the groin injury that has kept him out of action for the whole season.
Ian Holloway's side go into the game four points behind their opponents and are looking for a repeat outcome of September's meeting between the clubs, as Glenn Murray's second-half hat-trick saw Palace come from two goals down to win 3-2.