Another man went on to block the camera before he was pushed aside as the live link was cut. News anchor Ros Childs said: "We'll perhaps go back to Edith when the minute's silence has been completed."
A subscriber to the Vigilante News, an online news site with more than 123,000 followers, reportedly filed an official complaint with the ABC over the incident.
"I'm writing in to express my deep sadness and concern at the action of your staff today at the Hobart Invasion Day rally," the letter states.
" … Mid minute of silence, Edith chose to start reporting her prepared script.
"Once the silence had concluded and the speeches started again, a lady confronted Edith about her poor choice and timing. The cameraman came forward and tried to shove the lady out of the way to try and keep filming.
" … No apology was given to the people who called out this action by either the reporter, cameraman, or producer.
"I would like to know how such a respected news outlet as ABC lets producers and news teams make such deeply disrespectful and insensitive decisions. Would any member of your team start their talk to camera during the minute of silence for Remembrance Day?"
Agnes Forrester tweeted: "Not sure who at the ABC thought crossing to the Hobart Invasion Day rally during their minute silence was a good idea. Went about as well as you would expect. Use your brains broadcasters".
"Completely avoidable, rude, disrespectful and poor journalism."
Amber K posted: "so stupid yapped the whole way through the minutes silence ... what a genius", while another Twitter user described the act as "pretty bloody ordinary".
Some defended Bevin, with one writing: "Good on you for ignoring that moron and kept on talking".
Another added: "Please! It's a live national broadcast. Wasn't timed or malicious. Great work Edith."
The ABC has been approached for comment.