Noone, who joined Cardiff from Brighton in 2012, was hurt during last Saturday's 3-0 home defeat to Crystal Palace.
The 26-year-old is definitely out of Saturday's visit to Southampton and is likely to miss the remaining fixtures with Stoke, Sunderland, Newcastle and Chelsea.
"It's a big blow because Craig has been a player who's made things happen for us," said Cardiff boss Ole Gunnar Solskjaer.
"We've just got to find out how severe it is. It's very unfortunate because he has been terrific.
"But that's football. Sometimes you can't pick everyone you want. Every team has injuries."