The fire reportedly destroyed five mummified bodies in the church's historic crypt, including an 800-year-old mummy known as "The Crusader."
Topiter was taken into custody and has been charged with criminal damage to mummified remains. He faces a maximum of 10 years in prison if convicted and will appear before the Cloverhill District Court via weblink next week.
Authorities identified Topiter as the alleged suspect after he appeared on surveillance video footage behind a locked gate at the church. He was later arrested in the vicinity of the area, police said.
Archdeacon of Dublin and Vicar of St. Michan's Church, David Pierpoint, told RTE that the incident was "disastrous for Dublin, for history, and for the parish."
"The parish depends on income from our tourists and if we've no crypts to show people, then we have very little money coming in," he said. "We're not sure what's going to happen."
Archdeacon Pierpoint added that the mummified bodies have been "damaged beyond repair." Pierpoint said he would ask a National Museum to analyze the remains in the crypt, hoping that the museum might "salvage something."
"But we're really pretty certain that they've been destroyed," said Pierpoint.
Police asked the judge to hold Topiter without consent to bail due to the seriousness of the offense, with Garda James Kennedy explaining that "priceless historical artifacts of national importance" had been irreparably damaged.
Kennedy also told the court that Topiter acted "erratically and aggressively" during his detention, and are looking into inquiries about his Romanian national identity.
However, Topiter's defense attorney told the court that the suspect has been engaged to an Irish woman for the past four years and has significant ties to the country.
Judge Shalom Binchy granted a €10,000 bail in addition to a €2,000 cash deposit requirement. As a condition of release, Judge Binchy ordered Topiter to give up all travel documents, avoid going near St. Michan's Chuch, avoid talking to witnesses, and maintain sobriety in public.
The Church of Ireland Archbishop of Dublin, Dr. Michael Jackson, said he believes the "irreversible loss is something that will sadden generations, not only people of Dublin and school groups, but international visitors who make a point of coming to St. Michan's when they come to Dublin because they experience something unique."
"It's partly got to do with the climate, it's partly got to do with the conservation, but the fact that people who were a part of the Crusades were buried here and now it seems that option will not be open for them," said Archbishop Jackson.
He added, "The devastating impact on the opportunity to engage with something that is of history and fascination to people has now been taken away from us."