Derek Phin, 46, posted the comment because he believed the soldier's killers were being protected by the authorities.
Fusilier Lee Rigby was off duty in south-east London when he was brutally attacked and killed on May 22 last year.
Radical groups then tried to exploit the soldier's murder - resulting in attacks and protests against Muslims.
Phin, of Aberdeen, posted a comment on Facebook stating that Edinburgh Central Mosque should be burned down on July 2 during a demonstration.
The post, on a page belonging to the Scottish Defence League, read: "Burn the mosque down when the meeting is ongoing".
The mosque was due to be packed at the time for a meeting organised by pressure group Unite Against Fascism in response to extreme right-wing protests.
Police confronted Phin at his home in Aberdeen on September 4 after receiving a tip-off about the comment, which was posted last June.
He later admitted making the post online and stated to officers that he was a member of the Scottish Defence League.
The Scottish Defence League member appeared before Sheriff Annella Cowan at Aberdeen Sheriff court yesterday for sentencing.
Phin had pleaded guilty to posting the threatening and abusive remark with religious prejudice during a previous court appearance. And the former mail-room worker looked shocked in the dock as Sheriff Cowan jailed him for one year.
She said: "Justice in this country is measured and considered. Everyone in this country is entitled to the same freedoms and protections.
"You have abused what you think is your right to free speech to threaten the safety of innocent people in their place of worship because of your mistaken understanding of what they or their co-religionists stand for.
"Nothing other than a prison sentence is appropriate."
Defence agent David Sutherland said yesterday that Phin led an isolated life living with his parents.
He said his client had a "past-time" of looking at examples of terrorism online - material covering the Twin Towers attack and the London bombings.
Mr Sutherland said: "The comment came from what he thought extremists had done over a number of years. His response was to post this comment. "My client accepts it was unacceptable and inexcusable. He has already lost his job because of that."
Mr Sutherland added: "He's not accessed any of that [material] since this case last called."
Michael Adebolajo and Michael Adebowale were found guilty of the fusilier's murder at the Old Bailey on December 19 and were given life sentences earlier this week.