The 30-year-old defender was forced off at half-time in the Bluebirds' 1-1 draw with Derby with an ankle injury which forced him to miss the victory over Sheffield Wednesday.
"There is a complication and that's something we are looking into," manager Malky Mackay told the South Wales Echo.
"There are conversations needed with our medical people and I can't put a timescale on when Mark is back.
"It looks at least three or four weeks, but we still have to make decisions."
Mackay loaned in Norwich defender Leon Barnett last week and the former West Brom man looks likely to be a regular in the skipper's absence.
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- Malky Mackay