A spokesman for Communications Minister Mitch Fifield told the ABC that questions had begun to be asked about the outage.
The outage took place on Friday morning and was put down to a lightning strike by the telco.
By evening the same day, Telstra claimed that the situation was slowly returning to normal.
"The Department will seek information from Telstra and assistance from the [Australian Communications and Media Authority] in the conduct of the investigation."
The cable damage also affected Telstra's mobile voice services in NSW, Queensland, Victoria and South Australia between 2.05am and 4.50am AEST on Friday.