The unnamed employee was fired after Netflix learned about the data theft on April 4, the company said in a that was published online this week.
The worker "accessed over approximately the past two months, without authorization, the credit card information of some Netflix customers who spoke with the individual over the telephone," Netflix Senior Counsel Sharon Williamson wrote.
The employee obtained customer names and credit card numbers, she wrote. Netflix is investigating the incident and has notified police.
On Wednesday, Netflix declined to say how many customers were affected or whether any incidents of fraud had resulted from the theft.
"We do everything we can to safeguard our members' personal data and privacy, and when there's an issue like this we deal with it swiftly and decisively," said Steve Swasey, a Netflix spokesman.