"Sudden arrival of an invader from another land, decimating populations, creating terror. Forces the population to make enormous sacrifices & completely change how they live in order to survive. COVID-19 or Cook 1770?" she tweeted on Wednesday.
Mr Morrison said he found the comments "very disappointing".
"She clearly wouldn't get the job as chief historian," he told 2GB radio on Friday.
"I applaud the work she is doing as a medical officer in Victoria, that's her expertise. I would strongly suggest she keep to that, because those sort of comments don't inspire confidence.
"People should stick to their day jobs."
Home Affairs Minister Peter Dutton accused Dr van Diemen of running "culture war debates", and declared: "She is unfit for that office and she should go."
"It's pretty obvious in the middle of a pandemic the second highest medical officer in the state of Victoria should be concentrating on the people of Victoria and the crisis associated with COVID-19," he told the Nine network on Friday.
Victorian Liberal MPs, including Opposition Leader Michael O'Brien, have also criticised the tweet.
"Premier, please ask your health officials to get back to work to give us a pathway out of your lockdown - instead of giving us woke political commentary on Twitter," Mr O'Brien tweeted.
Federal Labor MP Richard Marles said the tweet was "unhelpful", but argued Dr van Diemen should not be stood down.
But Victorian Premier Daniel Andrews spoke out in support of his health official at a press conference on Friday morning, saying the tweet had been posted on Dr van Diemen's day off and if politicians had "time to go to these matters then good luck to them".
He said his time was better spent on the health crisis itself.
"People have died, so many people are out of work, we're a long way from the end of this, that's what's dominating my thinking, not tweets. If people want to find fault with that, fine," Mr Andrews said.
"I don't believe that's the most important issue today. My priorities are very clear and that's not changing."
"I've got no comment to make on any member of the public health team other than thank you for the work you are doing because it is making a massive difference," he said.
"They have all been working very, very hard, working long hours for all of us."
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