Anderson was due to preach to a congregation in Dublin later this month.
A Change.org petition calling for him to be barred from the country gained over 14,000 signatures.
Exclusion orders went into effect in 1999, allowing the minister for justice to proceed if he or she "considers it necessary in the interest of national security or public policy".More news: Florida shooting reportedly involving local rapper NBA YoungBoy
Pastor Steven L. Anderson runs a small Baptist church in Arizona and has become notorious for his extremist views.
It is the first time the Irish government has used the legislation to bar anyone from the country.
Addressing Minister Flanagan, the LGBT Ireland Twitter page posted a tweet that reads: "We are very thankful for your decision today to ban Steven Anderson from Ireland".
After 49 people were killed in a gay nightclub in Orlando, Florida, Mr Anderson told his audience the victims "deserved to die in the shooting".More news: Lionel Messi left Anfield in tears following Barcelona's drubbing by Liverpool
Mr Anderson has 10 children and set up the church on Christmas Day, 2005.
The Tempe church leader's inflammatory comments have included praying for then-President Barack Obama's death and denying the Holocaust happened. "We are an old-fashioned, independent, fundamental, King James Bible only, soul-winning Baptist church". They claimed Mr Anderson has "advocated exterminating LGBT+ people".
As well as Ireland, Anderson has also been refused entry to all other 26 European Union member countries.
The pastor is also banned from South Africa, the United Kingdom and the Netherlands, which he planned to visit May 23.More news: Elon Musk's trail date set for 'pedo guy' tweet
His biography states that he holds no college degree but has "well over 140 chapters of the Bible memorized word-for-word, including approximately half of the New Testament".
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