The 30-year-old centre-back had to be withdrawn in the victory over Wolves and scans suggest the defender will be sidelined for meeting with Middlesbrough and the visit of Derby.
Hudson, who had only previously missed one npower Championship game, could be replaced by Cardiff youth product Ben Nugent who stood in when Ben Turner was sidelined earlier in February.
But the youngster has missed the last two games with an injury to his leg so Malky Mackay may shuffle his defence with Kevin McNaughton coming in at right-back and Matt Connolly partnering Turner.
Meanwhile Rudy Gestede and Jordon Mutch both netted for the Bluebirds' development side in midweek to hand a timely reminder to the watching Mackay.
The Bluebirds sit eight points clear at the top of the table with 13 games to go.
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- Malky Mackay