The health insurer revealed on Wednesday it had received messages from the alleged hackers claiming they had removed customer data, less than a week after it was hit by a cyber attack.
An investigation has been launched, with federal government agencies examining the incident and working alongside Medibank.
Ms O'Neil said the situation was concerning and that agencies were working to stop the data from being released on the internet.
The Medibank hack, following the recent widespread data breach at telecommunications company Optus, is a wake-up call for business.
"This is the new world that we live in, we are going to be under relentless cyber attack essentially from here on in," the minister told ABC Radio on Thursday.
"We need to do a lot better as a country to make sure that we are doing everything we can within organisations to protect customer data and also for citizens to be doing everything they can."
Ms O'Neil said it was too early to tell how many customers had been affected by the Medibank hack after speaking with the insurer's CEO.
Medibank is now working alongside federal police and the Australian Signals Directorate to manage the breach.
"The reason that I am so concerned about this at the moment is because, of course, of the sensitive nature of the information involved," Ms O'Neil said.
"What we have here is information that's held by this organisation, which is healthcare information, and that just on its own being made public can cause immense harm to Australians."
The Australian Securities Exchange-listed Medibank went into a trading halt after it was contacted by the alleged hackers.
"Medibank systems have not been encrypted by ransomware, which means usual activities for customers continues," it said in a statement.
"We continue to work with specialised cyber security firms and have advised the Australian Cyber Security Centre."
31°C