The 4,600-year-old grave contained the remains of a man, woman and two youngsters, and DNA analysis shows they were a mother, father and their children.
"Their unity in death suggests unity in life," researchers said in Tuesday's edition of Proceedings of the National Academy of Sciences.
While tools and remains from the stone age have long been studied, there are few clues to the social relationships between people.
"By establishing the genetic links between the two adults and two children buried together in one grave, we have established the presence of the classic nuclear family in a prehistoric context in Central Europe - to our knowledge the oldest authentic molecular genetic evidence so far," lead author Wolfgang Haak of the University of Adelaide, Australia, said in a statement.
The researchers studied four multiple burials at Eulau, Saxony-Anhalt, all dated to the same time and containing adults and children carefully buried facing each other.
Several of the skeletons showed evidence of injuries, suggesting a violent attack. There was a stone projectile point in the vertebra of one woman and another had a skull fracture. Several had forearm and hand injuries, indicating attempts to protect themselves, the researchers said.
The scientists suggested that survivors of the raid later returned to bury the dead.
Besides the nuclear family in one grave, a second grave held three children, two of which were siblings, buried with a woman to whom they were not maternally related. The researchers think she may have been a paternal aunt or stepmother.
The team also looked at the strontium levels in the teeth of the skeletons. Strontium builds up in teeth during childhood and can be a clue where someone was raised.
Alistair Pike, head of archaeology at the University of Bristol, said the strontium levels showed that the females grew up in a different area from the males and children. That is an indication of marriage between different groups, with women going to join their husbands, which would have been important to avoid inbreeding and to forge kinship networks with other communities.