But for those who choose to take part he said there will be benefits for efficiency and access to medical records, he believes.
The system has been in place for six years and already six million Australians are participating.
People have been given a three-month window from July 16 to October 15 to opt-out if they don't want to be involved before a record is created for those remaining.
Labor has called on that deadline to be extended to allow the government to run an information campaign to restore public trust in the scheme.
About 20,000 people opted out on the first day of that period, fearing the risk of privacy breaches.
In a letter to Health Minister Greg Hunt, opposition health spokeswoman Catherine King reiterated Labor's support for digital health records, but raised concerns the government's implementation process had "seriously undermined public trust".
She accused the government of failing to effectively communicate potential benefits and to explain how people's rights will be respected and privacy protected.
"This approach has fuelled suspicion and scepticism - which may be why tens of thousands of people have rushed to opt out in the first week," she said.
Her colleague Anthony Albanese declined to say whether he would opt-out or remain but questioned the government's digital competence.
"They stuffed up the census, we know that some previous records relating to health were made available to people when it shouldn't have been so certainly the government, when it comes to competence, has stuffed up a whole range of things," he said
A spokesman for Health Minister Greg Hunt said Australians could opt out of the scheme at any time, even after the October 15 deadline when a record has been created for them.
"The opt-out approach is overwhelmingly supported by consumer health groups in Australia," the spokesman said.
The government was investing $114 million to explain the system to consumers, GPs, pharmacists and other stakeholders.
"My Health Record is subject to some of the strongest legislation in the world to prevent unauthorised use and backed up by a world-leading cyber security team," he added.
Mental health bodies and lobby group Digital Rights Watch have urged people to opt out if they doubt the security of the system.
The nationwide rollout comes as the Turnbull government was ranked number two in the world for delivery of online services by the United Nations.
Australia has been in second position since 2014 and was this year topped by Denmark, replacing the UK which moved to fourth.