The data, which relates to customers of its time-share division, Marriott Vacation Club International, included personal information such as the credit card details, Social Security numbers and, in a few cases, the bank details of customers.
The company said it has contacted the affected customers and is offering to enroll them free-of-charge in a credit-monitoring service so that customers can discover if there is any irregular activity on their account.
"We regret this situation has occurred and realize this may cause concern for our associates and customers," said Stephen Weisz, the president of Marriott Vacation Club.
The company has launched an investigation into how the tapes disappeared.
Customers of Marriott Vacation Club who are concerned that they may have been impacted can find out more information from the company Web site.
Ingrid Marson of ZDNet UK reported from London.