In the video, a man in a balaclava claiming to be from neo-Nazi group Warriors for Convict Resistance reads a statement from his phone endorsing "white Australia".
He then makes racist statements about First Nations people before burning the Indigenous flag and performing a Nazi salute.
The Australian Federal Police were made aware of the video on Tuesday when it was posted to X, formerly known as Twitter.
It has since been taken down and the account that posted it has been de-activated but the AFP is continuing to investigate the matter.
The video is just one instance of a growing trend of threatening communications sent to politicians.
"Reports of harassment, nuisance, offensive and threatening communications against parliamentarians/electoral offices have increased in the past two years, including via social media," an AFP spokesperson told AAP.
"Threats of harm or violence against Australian high office holders are criminal offences, and will be fully investigated by the AFP."
Federal government frontbenchers condemned the video.
"It's cowardly and disgusting," Labor's Bill Shorten told Nine's Today Show on Thursday.
"I don't know what it is with these man-baby Nazis - wearing a hood so no one can see you. They think they're so tough."
Home Affairs Minister Clare O'Neil spoke in support of Senator Thorpe, a Gunnai, Gunditjmara and Djab Wurrung woman from Victoria.
"That video is menacing, disgusting, and it is obviously deliberately targeting her to stop her from expressing her views," she told Nine.
"We will do everything we can to support Senator Thorpe."
With the referendum on the Indigenous voice to parliament to be held on October 14, politicians are growing more concerned about extremists spreading racism and misinformation.
"I am really worried about it," Ms O'Neil said.
"We're seeing over time in Australia different types of groups who pop up, selecting different ideologies ... being radicalised and joining these communities online, working together and getting more violent in their radical activities."
The minister expressed faith in Australia's security agencies, saying they are "very, very, very good at what they do".
"They watch these groups very closely and it is a big focus of our government to make sure we stay on top of these problems."
This is not the first time Senator Thorpe has been threatened by neo-Nazis.
A similar video created by the same neo-Nazi group in February 2022 used a racial slur against the Blak Sovereign Movement leader and showed the Indigenous flag being burned.
Senator Thorpe is expected to speak about the video later on Thursday.
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