Teiresias and Oedipus are the two blind characters. Teiresias is blind, however, he possesses knowledge, wisdom and restraint. Oedipus blinds himself after refusing to accept Teiresias' advice and wisdom.
In the terrible knowledge that he has fulfilled the prophecy, Oedipus blinds himself and in doing so suggests that he has seen too much - too much misery, too much foulness, and too much guilt. In blinding himself, he cannot undo or erase the knowledge he has gained. Like Teiresias, Oedipus now lives in a state of knowledge and blindness.
Given this connection, we might argue that blindness has an ironic relationship to knowledge in the text. Those who are blind have enough humility and wisdom to realize that people often do not "see" what is right in front of them. Teiresias says as much here, speaking to Oedipus:
"But I say that you, with both your eyes, are blind:/You cannot see the wretchedness of your life,/Nor in whose house you live, no, nor with whom."
Sight (as a symbolic representation of pride or power) is itself a form of blindness.