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.