According to a notice and open letter posted on the company's site on Wednesday, it has informed customers of the situation and that guest information may have been accessed, including credit card numbers.
While Radisson is not saying how many hotels or customers are affected by the incident, it is advising that all guests review their account statements and report unauthorised purchases to the bank that issued the payment card, as well as law enforcement authorities.
In a statement, Fredrik Korallus, the company's executive vice president and chief operating officer, said: "working with law enforcement and forensic investigators, we are conducting a thorough review of the potentially affected computer systems and have implemented additional security measures designed to prevent a recurrence of such an attack and to protect guest privacy."
The Radisson group - which operates more than 400 hotels in 68 countries - is headquartered in Minneapolis.