It is the first time on record that a Premier has been ejected from the Tasmanian Parliament.
Ms Archer took the highly unusual action while the Premier was being quizzed about what he knew about an incident at Ashley Youth Detention Centre.
Footage shows Mr Hodgman sparring with shadow attorney-general Lara Giddings across the chamber.
“Ask me a question and I’ll answer it,” Mr Hodgman tells Ms Giddings, who can be heard yelling, “I did ask you one!”
Mr Hodgman responds: “Well, ask me another one,” before the Speaker cuts him off.
“Right, the Honourable Premier is ejected, till 12 noon today. I’m not having that disrespect,” Ms Archer said.
It comes after Ms Archer was again overlooked for a ministry, with Guy Barnett instead promoted to Resources Minister last month.
Mr Green suggested it would exacerbate tension within the Government’s ranks.
“It seems as though there’s an enormous amount of tension in the Government,” he said.
No one is above the rules: Archer
In a statement, Ms Archer described the behaviour of all members as “highly disorderly”.
“No Member of the House of Assembly is immune from the Standing Orders, and I will always rule on matters as I see and hear it,” she said.
Government frontbencher Michael Ferguson dismissed suggestions it was evidence of tension within Government, describing it as all part of the “hurly burly” of Parliament.
While members of the Opposition parties regularly raise the Speaker’s ire with constant interjections, it is the first time a Tasmanian Premier has been booted from Parliament in at least 20 years, according to records.
He was not the only one to clash with the Speaker during Question Time, with Greens Leader Cassy O’Connor forced to withdraw a comment.
She had accused Mr Barnett of being a “climate criminal”, to which he took offence. Ms O’Connor withdrew it and replaced it with “climate vandal”.\