Cr Tully said patients of The Cedars Medical Centre on the corner of Queen and Church streets were unable to access their records to take to other doctors.
"You could really have some serious issues here," he said.
"We're talking about the medical records of hundreds of people, and a lot of them are elderly and need to see a doctor quite regularly.
"This is a real scandal and could be placing the lives of dozens of patients at risk."
Cr Tully said a "distraught" Bellbird Park man had contacted him asking for help.
"This patient cannot access his medical records to transfer to his new doctor to facilitate ongoing medical treatment," he said.
"If necessary, the law should be changed to enable immediate access to such records in these circumstances."
An Australian Medical Association spokeswoman said it was up to patients to retrieve their records. "There is no law in Queensland that says how long your doctor needs to keep the records for," she said.
"If patients can't get in touch with their doctor or the practice, it can be quite difficult for them to get their records.
"In that case they would have to contact the landlord, or if they go to another doctor they could ask them to make contact with their old doctor."
The Cedars, which included a bulk-billing doctor's surgery and Goodna Z-Ray facility, closed without warning last week.
A handwritten note taped to the centre's front door reads: "Due to unavoidable circumstances we are closed", while a recorded phone message says the practice is "temporarily closed".
Goodna X-Ray is permanently closed and its phones have been diverted to a practice in Richlands.
Staff who contacted The Queensland Times said the doctor's surgery was due to reopen on December 14.