The last known prosecution in Ireland related to blasphemy was thought to be in 1855, said Enda Kenny, the previous taoiseach, or Ireland's prime minister and head of government.
Mr Flanagan has now been given approval by the Cabinet to hold a referendum in October.
The Irish government has approved the preparation of a bill to remove blasphemy as part of a commitment to constitutional reforms. The referendum will probably be held on the same day as the presidential election.
"In terms of Ireland's global reputation, this is an important step", said justice minister Charlie Flanagan in a statement. "Regrettably, there are some countries in the world where blasphemy is an offence, the punishment of which is being put to death".
"They're a real threat to the lives of those who do not share the views of those enforcing the laws".
"By removing this provision from our Constitution, we can send a strong message to the world that laws against blasphemy do not reflect Irish values".
In Ireland, blasphemy against Christianity is prohibited by the constitution and carries a maximum fine of €25,000.
In 1937, the law on blasphemy was written into Article 40 of the constitution, which states that the "publication or utterance of blasphemous, seditious, or indecent matter is an offence which shall be punishable in accordance with law".
Ireland's current legislation makes it illegal to say or publish anything that is "grossly abusive or insulting in relation to matters sacred by any religion".
An investigation was launched into Fry after he blasted God as an "utter maniac" during an interview with Irish broadcaster RTE. It took two years until the police stopped the probe.