Senator Bernardi, a long time factional rival of Mr Pyne's, proposed the examination of how the Cabinet Minister's twitter account was hacked in the early hours of Thursday morning.
Opposition leader Bill Shorten yesterday said the hack was serious.
The Defence Minister this morning tweeted that he was hacked and questioned whether someone was 'making mischief over the plebiscite?'
One independent senator, Cory Bernardi, said it should prompt a "full investigation and report in case [it is a] foreign agent trying to influence elections".
"It's a good reminder to us all, quite frankly".
"We're satisfied that this is a public Twitter account, there's no connection between the Twitter account and Christopher's Defence portfolio", had told the Nine Network's Today Show.
Many users compared it to a similar incident in September where U.S. senator Ted Cruz's Twitter account "liked" a pornographic video.
An Australian politician's official Twitter account "liked" a gay porn video, just hours after the results of the same-sex marriage survey were announced.
'Deeply concerned about national security implications of hacking of Pyne's social media account, ' Mr Bernardi wrote on Twitter.
He said he was asleep when the Twitter activity took place.
Others raised concerns over the fact that the Minister for Defence Industry, a high-profile figure in government, could be hacked in the first place.
It came after United States Republican Senator Ted Cruz was also forced to explain his account "liking" a pornographic post in September. Mr Cruz told reporters the incident was a "staffing issue" and "not malicious".