Events leading up to the 1996 mass shooting, in which 35 people were killed, are the subject of the movie NITRAM, slated for release on streaming service Stan next year.
"I feel highly uncomfortable about this and I think many Tasmanians will," Peter Gutwein said on Tuesday.
He said the state government had not been contacted by the film's producers but it would not be right to censor the movie altogether.
"It is a difficult circumstance for many in our community," Mr Gutwein said.
I would hope the filmmakers are being sensitive in the way they shoot this particular production.
The feature is being made by director Justin Kurzel and writer Shaun Grant, the pair behind True History Of The Kelly Gang and Snowtown.
American actor Caleb Landry Jones will play killer Martin Bryant, who is serving a lifetime jail sentence in Hobart without the possibility of parole.
The movie has been filmed in Geelong and is being produced in Victoria.
A description on Stan says it will look at "events leading up to one of the darkest chapters in Australian history in an attempt to understand why and how this atrocity occurred".
Labor state opposition leader Rebecca White said the massacre should not be dramatised or turned into entertainment.
"It is a sensitive and traumatic history and a human tragedy that is still being lived by the Tasmanian community," she wrote on Facebook.
"The interests of victims of the Port Arthur shooting, survivors and their families as well as emergency service workers need to remain our highest priority.
"It is very unclear how their wellbeing will benefit at all from the production of a film."