David Coburn, a Member of the European Parliament for Scotland, has alleged that the nationalist supporter from Aberdeen made the threat on Facebook.
Mr Coburn, 55, has sparked outrage with many of his public pronouncements, including a claim that Alex Salmond would have been lynched in the event of a Yes vote.
An inside source revealed: “The threat relates to comments about shooting Mr Coburn in the face.
“Police Scotland are investigating an online threat and possible incitement received via David Coburn’s page.”
The source said the sender is believed to be a middle-aged father and former soldier from Aberdeen with SNP and Yes Scotland “connections”.
Arthur Misty, Chairman Ukip Scotland, said: “I can confirm an alleged hate crime against David Coburn MEP has been reported to Police Scotland.
“It is likely this is no more than the usual Braveheart bravado we have come to expect from cowardly keyboard commandos but we are not in the business of taking chances.”
He added: “I’m sure you will appreciate we do not wish to prejudice any investigation so neither David or I will be commenting further at this time.”
Commenting on the threat made against Mr Coburn an SNP spokeswoman said: “Abusive and threatening language is unacceptable.
“If Mr Coburn has reported this to the police, then it is rightly a matter for them.”
Mr Coburn has been a controversial character since he was voted into the European Parliament in May last year.
Earlier this month he sparked outrage after claiming former First Minister Alex Salmond would be “hanging from a lamppost” if there had been a Yes vote after the recent crash in the oil prices.
The openly gay politician has also spoken out about gay marriage, describing supporters of the law change as “equality Nazis”.
In an interview he said gay marriage only mattered to “some queen who wants to dress up in a bridal frock and dance up the aisle to the Village People”.
Meanwhile in September last year Mr Coburn was reported to have been overheard on an East Coast train speaking in less than flattering terms about Scottish politicians.
He was reported to have described Tory leader Ruth Davidson a “fat lesbian” and former Scottish Labour leader Johann Lamont as a “fish wife”.
The MEP, originally from Glasgow, later claimed to have no recollection of the conversation and reportedly said: “I’m a fat Scotsman, there so. I don’t recall any of this.”
He later denied the comment about the Scottish Tory leader but instead likened her to “porridge”.