State news agency ANA said at least two people, including a 50-year-old woman, were killed in a gunfire exchange in the mountainous village of Vorizia, some 52 kilometres (32 miles) southwest of the island capital Iraklio.
At least 10 more people were injured in the incident that involved AK-47 assault rifles and shotguns, state TV ERT reported.
The head of Greek police, other senior officers and reinforcements are heading to the remote area while on-site officers searched houses, state TV ERT said.
Police have not yet arrested anyone, and some of those involved are believed to have fled to a nearby ravine.
Heavily armed police had earlier surrounded the village so ambulances could pick up the injured, ERT reported.
The incident occurred hours after a house under construction in the village was targeted with an explosive device, ERT said.
Illegal gun ownership is rife on Crete, and family vendettas are common on the island. Guns are often fired to mark celebrations at weddings and festivals.
Last Sunday, 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, encouraged locals to avoid pointless gun violence, but to little effect.
AFP
