Anika Wells assured the public Telstra would "face the music" for its widespread network failure on Wednesday that affected communications, business, health and transport services.
"We will hold Telstra's feet to the fire so they feel your pain - what has gone on here is not good enough," Ms Wells told reporters in Canberra.
The government would not take a backward step "when it comes to holding telcos to account", Ms Wells said.
"Now that Telstra has resolved its outage, it is time for Telstra to face the music," she said.
The Australian Communications and Media Authority will launch an investigation into whether the company complied with its legal and regulatory obligations.
The telco had "let the country down", the regulator's deputy chair Adam Suckling said.
Telstra chief executive officer Vicki Brady earlier faced a barrage of questions about the telco's network failure after she cut short an international holiday to deal with the crisis.
"We have let our customers and Australians down, and for that I am deeply sorry," she told reporters in Sydney, hours after touching down.
"When something goes wrong, we're committed to taking accountability ... and fixing issues as quickly as possible."
A critical software fault caused the outage that halted train lines and timed out business transactions.
The national disruption forced Telstra to conduct 639 welfare checks on triple-zero users, with seven requiring assistance after initially failing to get through.
The ASX-listed behemoth was not responsible for a death of an elderly woman in South Australia on Wednesday, chief financial officer Michael Ackland said.
SA Liberal senator Kerrynne Liddle linked the death to Telstra's outage, but police have ruled this out.
"This is a distressing time for the family of the deceased woman. It is unfortunate their loved one's death was placed in the public arena in the manner it was when it need not have been,'' police said in a statement.
Ms Wells took a swipe at Senator Liddle for forcing police officers to verify the information with her after she posted the claims on her social media.
It is the third major national outage in less than a year for the $56 billion giant, which powers about 25 million Australian mobile services.
In May, Telstra sacked more than 100 people and merged two of its biggest technology divisions in a restructure, but Ms Brady denied job cuts had affected quality control systems.
"What I've seen so far is our people and our processes worked as they should have," she said.
Ms Brady said senior Telstra team members were affected by the outage and resorted to Microsoft Teams to relay the message about how thousands of customers were impacted.
The crisis has added to anger over Telstra's corporate leadership, with former federal treasurer Wayne Swan saying executive bonuses needed to be reconsidered.
Ms Brady deflected calls for her to slash bonuses of executives.
The outage was largely resolved by late Wednesday and a solution for a separate "secondary issue" that prevented some users making triple-zero calls was in place by Thursday afternoon.
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