The breach follows similar attacks at Hyatt Hotels and Starwood Hotels and Resorts Worldwide in recent months.
Connecticut-based HEI, which is privately held, said malware designed to collect card data was found on its systems.
The malware was discovered in early-to- mid-June on payment systems used at restaurants, bars, spas, lobby shops and other facilities at the properties, Chris Daly, a spokesman for HEI, said.
The number of customers affected is difficult to calculate because they might have used their cards multiple times, Mr. Daly said.
About 8,000 transactions occurred during the affected period at the Hyatt Centric Santa Barbara hotel in California, and about 12,800 at the IHG Intercontinental in Tampa, Florida, he said.
The malware affected 12 Starwood hotels, six Marriott International properties, one Hyatt hotel and one InterContinental hotel.
It was active from March 1, 2015 to June 21, 2016, with 14 of the hotels affected after December 2, 2015, HEI said.
Marriott and IHG declined to comment. Representatives from the other hotel groups did not respond to requests for comment.
HEI said outside experts investigated the breach and determined that hackers might have stolen customer names, account numbers, payment card expiration dates and verification codes.
The hackers did not appear to have gained PIN codes, it added.
The company has installed a new payment processing system that is separate from other parts of its computer network.