MacMillan took to Twitter to criticise the National Collective, which supports a break from the Union and the creation of a new nation.
He said: "I don't understand artists who suck up to Government politicians, or those who want to huddle in 'collectives' like Mussolini's cheerleaders."
MacMillan also raised the internet-based threats received by poet Gavin Bowd, who recently published a book on the links between Scotland and fascism.
In a further post to the National Collective, he said: "My careful assumption is that you know about poet Gavin Bowd's research into the fascist connections of your movement."
The National Collective responded by saying it had 1,200 members of varied political and non-political backgrounds ranging from 16-78. "Careful with your assumptions," it added.
The organisation also asked MacMillan not to include its user name in his Twitter posts unless it was relevant to do so.