The Seattle coffee giant sent an email to those who may have had details such as their names, dates of birth and phone numbers accessed an email, which stated there had been "unauthorised activity online" as well as "some unauthorised access to customer details".
However, credit card details were not leaked.
Starbucks is running an investigation with local authorities to establish how the security incident happened.
As reported by ZDNET, hackers claimed on September 10 to have gotten access to Starbucks Singapore's "full database".
Starbucks has now added more safeguarding features to its app.