The Wales left-back was hurt in a 16th-minute challenge with Craig Gardner as the players collided after going for the ball, with Taylor's lower leg awkwardly buckling under him as the pair fell to the ground.
Taylor was stretchered off after prolonged treatment and Laudrup said: "I just talked to the doctor and we are still not 100% but there is a fracture, at least one.
"We are talking about a long period of rehabilitation before he returns to the game, I can't tell you precisely how long because I don't know."
Sections of the home crowd were furious that Gardner was not punished for the challenge by referee Roger East, making his Premier League debut, although there appeared to be no malice on the part of the Sunderland player.
Taylor was in fact penalised over the incident, and Laudrup refused to cast any blame in the direction of Gardner.
"When you have injuries like that it is normally very violent, but this was not violent," he added. "It was even a free-kick against us. Sometimes these injuries happen in strange ways, you don't think anything is wrong and then there is ligament damage or something like that, it is very sad.
"But you see things that are much more violent than that - this was not violent, it was unlucky.
"He was very unlucky to fall in a bad way, you can't blame the Sunderland player for that."