Moore also said he would donate the royalties from sales of his new book, "Here Comes Trouble, in Georgia to the cause of ousting "the racists and killers who run that state."
Davis was put to death for the 1989 slaying of an off-duty Savannah police officer. Davis maintained his innocence to the end, and his supporters said the evidence used to convict him was dubious.
Moore said in a written statement he was asking "all Americans with a conscience to shun anything and everything to do with the murderous state of Georgia."
The Atlanta Journal-Constitution said the Georgia Chamber of Commerce had no comment on Moore's statement. A spokesman for Gov. Nathan Deal brushed it off, saying he doubted many copies of "Here Comes Trouble" would be sold in the state.
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