Bendtner suffered a broken nose when he was caught in the face by Swansea defender Angel Rangel's boot during Saturday's 2-0 Premier League victory over the Welsh side.
However, O'Neill has revealed that the damage is more extensive and as a result, Bendtner is likely to miss several games, starting with Sunday's FA Cup fourth round clash with neighbours Middlesbrough.
He told the Sunderland Echo: "He's got a bit more than a broken nose. It's difficult to put a timescale on it, but it's going to be lengthy. We thought at one stage he might be okay. The early signs, even on Sunday morning, were that it looked as if it might be okay.
"But he's going to be out for a number of weeks now, which is definitely a blow to us. He has a few cracks and we just have to bide our time with that. That's a big blow to us and to the lad himself, who was beginning to enjoy a decent spell of football for us.''
However, O'Neill is understood to have a interest in Bolton's Kevin Davies as the winter transfer window enters its final few days, although the Trotters have indicated they are not interested in a loan deal.