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.
"Yes unfortunately I am out for the rest of the season. The hamstring injury at Man U was worse than first thought," Hudson revealed via Twitter.
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.
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