Section 4 of the Act allows the Irish Government to sign an exclusion order if it "considers it necessary in the interest of national security or public policy".
Mr Flanagan said he had signed the order "under my executive powers in the interests of public policy".
The American self-proclaimed pastor from Arizona is a known Holocaust denier who has called for the killing members of the LGBTQ community and praying for the death of former United States president Barack Obama.
It is the first time the Irish government has used the legislation to bar anyone from the country.
Anderson is also a holocaust denier and has described homosexuality as an "abomination" and that is should be punishable by death. In 2014, he said that he prayed for the death of Barack Obama and that exterminating gay people could "cure Aids". It is not affiliated to any mainstream Christian churches across the world although Anderson claims his lectures have been translated into 115 languages.
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".
"This petition is for the people to show that they want Pastor Steven Anderson banned from entering the Republic of Ireland".
"We are an old-fashioned, independent, fundamental, King James Bible only, soul-winning Baptist church", it says.
Anderson has been banned now by over 30 countries, including all 28 in the European Union. He does not have a college degree but has "well over 140 chapters of the Bible memorised word-for-word", the website claims.