Security minister Tom Tugendhat said Rasmus Paludan, founder of the anti-Islam party Stram Kurs, had been added to the UK's immigration watchlist.
Mr Paludan had said he planned to burn the religious text in a public square in the West Yorkshire city this week.
It comes after four pupils at a Wakefield school were suspended over damage to a copy of the Quran.
In a video posted to Twitter on Sunday, Mr Paludan said he would travel to the city to "fight back" against "undemocratic forces".
He claimed he intended to burn the Quran on Wednesday to coincide with the start of Ramadan.
Mr Paludan has held several previous protests in which the Islamic text was burned, with some leading to violent counter-demonstrations.
In January he burned a copy of the Quran outside the Turkish embassy in Stockholm.
That protest became part of a diplomatic row between Turkey and Sweden - with Turkey now holding up Sweden's application to join Nato.
The security minister told the House of Commons about his intervention after Simon Lightwood, the Labour MP for Wakefield, raised concerns on Monday about Mr Paludan's potential visit.
Mr Lightwood said: "Far-right Islamophic Danish politician Rasmus Paludan said he is going to travel from Denmark to Wakefield for the sole purpose of burning a Quran in a public place.
"Mr Paludan was previously jailed in Denmark for his hateful and racist statements. He is a dangerous man that should not be allowed into this country.
"Can the home secretary assure me and my community that the government is taking action to prevent this?"
Mr Tugendhat said Mr Paludan had been added to to the UK's warnings index.
He added: "His travel to the United Kingdom would not be conducive with the public good and he will not be allowed access."
Four pupils were suspended from Wakefield's Kettlethorpe High School in February after a Year 10 student brought in a Quran, reportedly as part of a dare.
The cover of the Islamic text was torn and some pages scuffed, but police concluded no offences were committed and the school's headteacher said she was satisfied there was "no malicious intent by those involved".