They did not specify how the shooter died.
The shooting happened Sunday morning in the village of Martonos, close to the border with Hungary.
Police said the carnage was triggered by "unresolved family relations."
They said the man, in his mid-50s, fired multiple shots from a hunting rifle, killing six people aged between 24 and 74.
In 2013, a Balkan war veteran killed 13 people in a shooting spree in a central Serbian village.
The tragedy shocked the nation and sparked a public debate about the amounts of weapons left over from the 1990s conflict.