Mr Harvie reiterated his party’s opposition to the monarchy on Friday, saying an independent Scotland should have an elected head of state.
The royal family has been rocked by allegations of racism from the Sussexes, revealed publicly in an interview with Oprah Winfrey.
In a rare move on an official visit on Thursday, Prince William briefly spoke to reporters to say he had not yet talked to his brother.
He said: “We’re very much not a racist family.”
William’s statement was the first public personal comment by any member of the royal family since the allegations.
In a statement on Friday, Mr Harvie said: “The revelations from the last few days, and other recent scandals, raise serious questions about the attitudes and values of the royal family and those around them.
“They also serve as a reminder that the monarchy itself is an outdated, discredited and totally undemocratic institution.”
He continued: “As we look to the future that Scotland can have as a fairer, greener and independent country, it is clear that asking the people to choose a modern, democratically accountable head of state would be the best step forward.
“The idea that any family has the right to such status based on hereditary titles and unearned wealth would hold Scotland back, and it’s not one that the Scottish Greens will ever support.
“Their shooting and hunting estates can be put to better use serving the local communities and creating more jobs.”
Responding to the Greens, the Scottish Conservatives said the monarchy had wide support among Scots.
Tory MSP Murdo Fraser said: “The monarchy is one of our most loved and respected institutions and that is still widely recognised across Scotland.
“Patrick Harvie is indulging in the most pathetic type of politics in a shameless bid to pander to republican voters who might be tempted to vote for his party.
“The vast majority of Scots will recognise this patronising attempt to woo the electorate and see right through the Greens’ illogical nonsense.
“The benefits of having a constitutional monarchy as opposed to an elected politician as head of state are overwhelming.”