The arrest took place early Thursday following a police operation in the Prospect area, a police spokesperson said.
The 35-year-old man remains in police custody while enquiries continue.
Ms Baker, 25, was last seen on Saturday, 30 July and was believed to have been taken from her home in the Beach Bay area. Her car was found abandoned in Pedro Castle two days later.
Anyone who has any information in relation to the disappearance of Kerran should call George Town police station on 949-4222, the RCIPS tip-line 949-7777, or Crime Stoppers 800-8477 (TIPS).