Our Lady's Church on the Larne Road in the Harryville area has also been subject to sectarian paint and arson attacks over the years.
Protests outside the church began in 1996 and ended after the Good Friday Agreement.
The picket was originally mounted by loyalists in response to the RUC's blocking of an Orange Order parade through the overwhelmingly Catholic village of Dunloy.
The building, which has a unique hexagonal design, has developed a problem with leaking water causing damage which would cost an estimated £300,000 to fix.
Damp, damage to the roof and electrical failure mean the 45-year-old church will be demolished.
"The Church of Our Lady, Mother of the Church, was solemnly blessed and dedicated on 8 September 1968 by the Bishop of Down and Connor Dr William Philbin having been built on a site given to the parish of Kirkinriola," a parish statement said.
"For over 40 years together with our other church buildings it has served the spiritual needs of the people of the parish. Its distinctive architecture made it a special feature in Ballymena and its beautiful interior made it a place particularly suited to prayer and worship."
It continued: "For some time now the building has been unsafe and has had to be taken out of use in February 2012.
"The costs, coupled with an assessment of the current needs of the parish community, has prompted the parish authorities to close the church on a permanent basis.
"This decision has naturally been taken with regret on account of the fond memories and strong attachments that we all naturally have to a church building."
The statement said the congregation will be relocated to St Patricks, Crebilly in the town.