The central defender injured his hamstring against Manchester United in January, only his second league appearance of 2013/14, and will now play no further part of the term
The central defender, 31, injured his leg in the Welsh outfit's loss at Manchester United in late January, and his second league match for the 2013-14 campaign would be his last.
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It is further injury heartbreak for Hudson after undergoing ankle surgery in March last year.
Manager Ole Gunnar Solskjaer said: "He has had a very bad hamstring injury but we will get him back for next year."
Solskjaer also said defensive midfielder Gary Medel will be out for a fortnight, in another blow to Cardiff's prospects of avoiding relegation.
However, in positive news for the club, defender Kevin McNaughton has signed a one-year contract extension.