Health Connector Customer Service Call Center Phone: (877)-MA-ENROLL (877) 623-6765) TTY: (877) 623-7773 Hours: Monday - Friday: 8:00 a.m. to 6:00 p.m. Health Connector Walk-In Center Locations. Health Connector members can visit a walk-in center to complete a new application, make changes to your existing Health Connector account, plus.