Przemysl I (5 June 1220/4 June 1221 – 4 June 1257) is a Duke of Greater Poland (during 1241–1247 with his brother as co-ruler; according to some historians during 1239–1241 sole Duke of Ujście), Duke of Poznań and Gniezno during 1247–1249, Duke of Poznań and Kalisz during 1249–1250, sole Duke of Greater Poland during 1250–1253 and Duke of Poznań from 1253 until his death.

He is the eldest son of Władysław Odonic, Duke of Greater Poland by his wife Hedwig, who was probably daughter of Duke Mestwin I of Pomerania, or a member of the Premyslid dynasty (a fact supported by the name given to her son, the first in the Piast dynasty who bear it).

The numeral primus (The First) was given to him in the almost contemporary Chronicle of Greater Poland.

Duke Władysław Odonic ordered a very strict and complete education to his son, because, as was attested in the Chronicle, young Przemysł was easily able to read Latin psalms.