The quake was of magnitude 4.8 and a subsequent quake was 4.3.
According to the AP, people in panic must have moved out of their homes in connection with the incident.
The injured are said to have broken legs and head injuries.
One of the three dead is said to be a three-year-old girl.
The island, a popular tourist destination, reopened to tourists on Thursday.
This after being closed for a year due to the coronavirus.