It is the first such fatality since a Saudi-mediated ceasefire between the groups was signed a month ago.
The man was killed in the town of Beit Hanoun after a shoot-out between the two factions.
Each side blamed the other for starting the violence, which shook the town with mortars and rocket-propelled grenades.
Ambush claim
The clashes happened just hours after Prime Minister Ismail Haniya of Hamas said the members of a newly-agreed unity government would be announced in the coming days.
The Hamas fighter killed was identified as Mohammad al-Kafarna, a member of the group's Executive Force.
Hamas said that he was killed after Fatah fighters ambushed the vehicle he was travelling in.
But a Fatah spokesman said that shots had initially been fired by Hamas gunmen on a car carrying members of the al-Aqsa Martyrs' Brigade.
The agreement between the two groups, signed on 8 February in the Saudi city of Mecca, had brought a fragile end to factional fighting, which has claimed more than 90 Palestinian lives since December.
Photo caption
Funeral procession of Mohammad al-Kafarna