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.
Manchester United eyeing surprise move for AC Milan star for whom tension in Italy is growing: report
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
