The free public performance, held in Civic on Friday night as part of the Fringe Festival, featured a performer in a Nazi-style uniform wearing a Hitler moustache who stripped down to her underwear.
Mr Hanson labelled the performance “anti-Semitic”.
“There is simply no place for Nazi references at the National Multicultural Festival,” said Mr Hanson.
“The Chair of the ACT Multicultural Forum has described the act as ‘insulting’ and has called for those involved in the decision for this to occur to be made accountable.”
Mr Hanson added Ms Burch was “blunder prone”.
In November she was forced to apologise after she re-tweeted an offensive Twitter post that labelled federal Education Minister Christopher Pyne ”a c–t”. She also sparked controversy last year when she appointed Jorian Gardner to direct the Fringe Festival without a competitive selection process.
“The ACT can’t afford any more instances of poor judgement by Joy Burch. This time she has gone beyond causing embarrassment to herself and the government and she has insulted members of our own community. It’s time for her to leave the ministry before she does any further damage,” Mr Hanson said.
“The Chief Minister must step in and apologise to members of our multicultural community who have been insulted, she should condemn this offensive act and she should stand Ms Burch down as a minister”.
But Chief Minister Katy Gallagher says the government did not receive any complaints about the performance, and would not “get into censoring art”.
According to Ms Burch, the audience were “advised of the adult nature of the show.”