The 42-year-old suspect put the clip, entitled “Consider your neighbour: it stinks when it burns" to a group called “YES TO FREEDOM – NO TO ISLAM” in December 2015.
Jan Reckendorff, from the public prosecutor’s office in Viborg, said: “It is the prosecution's view that circumstances involving the burning of holy books such as the Bible and the Quran can in some cases be a violation of the blasphemy clause, which covers public scorn or mockery of religion.
“It is our opinion that the circumstances of this case mean it should be prosecuted so the courts now have an opportunity to take a position on the matter.”
Judges in Aalborg will heard the case, although a date has not yet been set.
The maximum sentence for blasphemy is four months in prison but Mr Reckendorff said prosecutors were more likely to seek a fine.
Copies of the Quran are treated with reverence by Muslims and any move to desecrate or destroy the holy book is seen as a grave insult.
Rumours of Quran burnings have sparked arrests, lynchings and riots in Muslim-majority countries, while the move has been appropriated by the far-right and anti-Islamic groups, including the Westboro Baptist Church in America.
Under clause 140 of Denmark’s penal code, anyone can be imprisoned or fined for publicly insulting or degrading religious doctrines or worship.
Only four blasphemy prosecutions have ever been attempted in the country.
The last was in 1971, when two Denmark Radio producers were acquitted after airing a song mocking Christianity.
Two people were previously fined in 1946 after acting out a “baptism” at a ball in Copenhagen, while four others were sentenced for putting up anti-Semitic posters and leaflets in 1938.
At least a dozen other cases have been considered but not charged, including in 2006 when prosecutors decided to stop an investigation into the Jyllands-Posten newspaper over a controversial set of caricatures under the headline “The Face of Mohamed”.
The publication sparked protests around the world, with insulting the Prophet seen as a grave offence to Muslims and Islamic scholars interpreting Quran verses on idolatry to forbid any representation of Mohamed.