Vibullia was a Greek of Athenian descent and was a member of a very wealthy family who were prominent in Athens. She was the daughter of the Athenian Aristocrats, Claudia Alcia and Lucius Vibullius Rufus. She had a brother Lucius Vibullius Hipparchus, who served as an Archon of Athens in 99-100. Vibullia was born and raised in Athens.
Vibullia bore Claudius Atticus three children who were:
Herodes Atticus with his wife, the Roman Aristocrat Aspasia Annia Regilla, had erected a great outdoor nymphaeum (a monumental fountain) at Olympia, Greece. The monumental fountain features statues and honors members of the ruling imperial family, relatives of Herodes Atticus and his wife. Among the statues is a statue of Vibullia. The statue bust of Vibullia is on display at the Archaeological Museum of Olympia.