Late on Wednesday night, Mr Rockliff posted on Facebook that he was aware of "efforts made to remove all references to Christmas in end-of-year school celebrations".
"Acknowledging other traditions is important. But that's not a reason to abandon our own," the Premier wrote. "Christmas is a time that brings us together. And our school kids should be encouraged to sing Christmas carols whenever they please. I have requested that the education department step in."
The post did not name a school, but commenters and other media identified Trevallyn Primary School in Launceston, as well as its acting principal.
In a newsletter to families dated October 2, the school said its December fundraising raffle, "formerly known as Christmas on the Hill", would now be called the "End of Year Extravaganza!". The school's calendar in the same newsletter still makes multiple references to Christmas, including planned carols and a Christmas celebration at Tailrace Park, and currently lists "TPS Christmas Carols" on December 10.
Mr Rockliff also sent a letter to education department secretary Ginna Webster naming the school and referencing correspondence he had received from a parent, writing: "I do not support schools removing reference to Christmas in end-of-year celebrations or removing carols."
Australian Education Union Tasmanian state manager Brian Wightman told 936 ABC Hobart he was appalled by the Premier's actions, saying a public servant had been named and "the school shamed along with the school association".
"The consequences of this are significant and the psychological harm that the premier has caused is reprehensible," he said.
Mr Wightman said he had yesterday provided the principal's phone number to Mr Rockliff and urged him to hear the school's reasons for the changes before reacting. "It has been blown out of all proportion. The premier's actions are reprehensible and he must pick up the phone today and fix this," he said.