The England Under-21 captain was stretchered off after falling awkwardly while challenging John Obi Mikel.
He landed heavily on his arm and damaged his shoulder and wrist.
Although City do not know how long Onuoha will be out for, it seems unlikely he will be involved again this term.
"The shoulder was dislocated and then went back in," said City boss Sven Goran Eriksson.
"It was very painful and there is a wrist problem as well, he is in hospital and we don't know how he is just yet.
"It's a shame because he stood up to Chelsea and had played excellently before then."