State media reported that AK-47 assault rifles and shotguns were used in the attack in the remote village, about 50km southwest of the island capital Iraklio.
Hours earlier, a house under construction in the village was damaged by an explosive device.
Heavily armed police reinforcements were rushed from Athens, and the head of Greek police is personally heading the investigation.
Illegal gun ownership is rife on Crete, and family vendettas – frequently caused by perceived honour insults – are common on the island.
Guns are also often fired to mark celebrations at weddings and festivals.
Recently, a 23-year-old shot and killed a 52-year-old man during a village celebration in western Crete.
A campaign in 2005, backed by the late, legendary Cretan Greek composer Mikis Theodorakis to encourage locals to avoid pointless gun violence, had little effect.
- Agence France-Presse