The woman, who is a teacher by profession, wants the man to marry her colleagues at the school at the same time.
According to Saudi daily Al Youm, the would-be groom was shocked by her unexpected demand, but came under strong pressure from relatives and friends who eventually persuaded him to accept to marry the three women.
Under the deal, the bridegroom rented three apartments in the same building and lodged each of his brides in her own flat, Gulf News reports.
Polygamy is allowed in Saudi Arabia, and a man is entitled to take up to four wives.
The man, however, must not differentiate between them and must treat them equally physically and emotionally and in regard to sustenance, expenditure, time and all obligations as a husband.