She was the fourth daughter (twin with Anna) of Przemysł I, Duke of Greater Poland and Poznań, by his wife Elisabeth, daughter of Henry II the Pious, Duke of Wrocław. She was named after her paternal aunt Euphemia, wife of Władysław, Duke of Opole. In sources, and like almost all the Piast princesses who bear that name, Euphemia was also called with the diminutive Ofka.
