Rosneft Deutschland reported the incident in the early hours of Saturday morning, the BSI said.
Anonymous had published a statement on Friday claiming responsibility for the attack and saying it had captured 20 terabytes of data.
Prosecutors in Berlin have opened an investigation, according to a report in Der Spiegel magazine.
Rosneft Deutschland reportedly subsequently took its systems offline. Its pipelines and refineries continue to operate as normal, the report added.