Bendtner sustained the facial injuries when he was caught in the face by Angel Rangel’s boot during Saturday’s game against Swansea.
Sunderland manager Martin O’Neill 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.”
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