The person who has schizophrenia can get married, so long as he informs the woman he wants to marry about his illness. That is because every sickness or fault that may have an impact on married life or may put the wife off must be disclosed and it is haraam to conceal it.
Insanity is one of the defects that render the marriage contract null and void according to the majority of fuqaha’. If the woman is not aware of it at the time of the marriage contract, then she comes to learn of it afterwards, she has the right to annul the marriage.
See: al-Mughni, 7/140; al-Mawsoo‘ah al-Fiqhiyyah, 16/108
Ibn al-Qayyim (may Allah have mercy on him) said: The analogy is that in the case of any defect which puts one spouse off the other, and means that the aims of marriage, such as compassion and love, cannot be attained, the option to annul must be given.
End quote from Zaad al-Ma‘aad, 5/166
Shaykh Saalih al-Fawzaan (may Allah preserve him) was asked: My brother is epileptic, but this does not make him impotent. He has done the marriage contract with a woman; does he have to tell her about his sickness before consummating the marriage with her, or not?
Yes, each spouse must tell the other of any physical defects that he or she has before marriage, because this comes under the heading of honesty and because it is more likely to bring about harmony between them and ward off disputes, and so that each of them will enter into marriage with the other with full disclosure. It is not permissible to deceive and conceal.
End quote from al-Muntaqa min Fataawa al-Fawzaan
To sum up: the one who is affected by insanity or any other disease may get married on condition that he informs the one he wants to marry of his sickness.
And Allah knows best.