In the unverified screenshot, the employee in question writes of being a "professional stalker" searching for hackers.
In a statement, Facebook's Chief Security Officer Alex Stamos said the company quickly investigated the situation and immediately fired the person.
Access to sensitive data is logged, and the company has automated systems designed to detect and prevent abuse, Stamos said.
"Employees who abuse these controls will be fired - period."
The firing was first reported by the Wall Street Journal.
© Thomson Reuters 2018