Health authorities say 75,000 people received a notification through the ACT Digital Health Record related to historical records.
But they say only fewer than five people received messages about medical information that was not theirs.
The 75,000 people who received messages related to old test results and was due to old data being uploaded onto the system.
The issue affected those who had created their own accounts for the digital health record.
About 186,000 people signed up to the record to book a COVID vaccine or to receive care for COVID at home.
The digital health record, which went live on Saturday, collated all paper and digital records in the territory's public health system under the one electronic system.
The Canberra Times was made aware of people receiving alerts for upcoming appointments that were not theirs.
ACT Health said the error was caused because records had been inappropriately combined.
"On investigation, the new Digital Health Record system helped us identify that these records had been inappropriately combined," a government spokeswoman said.
"We have conducted a review of the remaining 75,000 records and have not identified any other records that experienced the same issue."
The spokeswoman said authorities had identified why this occurred and corrected the root cause.
ACT Health was asked whether the incorrect messages constituted a breach of the Health Records (Privacy and Access) Act.
In response, the spokeswoman said the issue came from people sharing their family members contact details.
"The reported instances have been investigated and found that people are sharing their family members' contact details (mobile phone and email addresses) when interacting with ACT public health services," the spokeswoman said.
"Primarily we have found family information was shared during registration for a COVID vaccination or treatment."
However, The Canberra Times is aware of one person receiving information about an appointment that was not theirs or was not a family member.
The spokeswoman said: "If anyone has received information that appears to relate to another person who is not a family member, we ask that they contact the DHR support line on 02 5124 5000 so that the matter can be investigated. The support line is open 24/7."
