Watch Ashling Murphy's loved ones pay tribute at her funeral mass in this UTV News report.
The 23-year-old school teacher was murdered last week while out for a run along a canal in Tullamore, Co Offaly.
The arrest came as hundreds of mourners attended the funeral mass for the teacher at St Brigid's Church in Mountbolus on Tuesday morning.
There her family were joined by Irish leaders and pupils from her school who held red roses and photographs in tribute to their teacher.
Irish police said the man is being questioned at Tullamore garda station in Co Offaly.
The body of Ms Murphy, a talented musician and teacher, was found on the banks of the Grand Canal in Tullamore last Wednesday.
Her death has intensified debate around women’s safety and prompted calls for more to be done to tackle gender-based violence.
The arrest was made after police renewed an appeal for information. The man, aged in his 30s, is being questioned on suspicion of murder.
Among the mourners at Ms Murphy’s funeral was Irish president Michael D Higgins and Irish premier Micheál Martin.
Minister for Justice Helen McEntee, Minister for Education Norma Foley, and Minister for Tourism Catherine Martin also attended.
Mr Higgins and his wife Sabina hugged Ms Murphy’s family at the funeral mass.
Symbols of Ms Murphy’s life were brought to the altar during the service, including a fiddle, a Kilcormac/Killoughey camogie jersey, a family picture, a school book, and her photo.
Bishop Tom Deenihan also addressed mourners on behalf of the Diocese of Meath, describing the past few days as "a nightmare" as he said her death had united the country in grief.
He told mourners: “A walk on a mild and sunny afternoon in January should be a happy event, promising the brighter and warmer days of spring and summer. That, as we know, was not the case."
Parish priest Michael Meade told Ms Murphy’s loved ones they had been “robbed of your most precious gift – a gift that gave only joy and love, fun and laughter to many, many beyond yourselves and bounds of your own home”.
Representatives from Ms Murphy’s local Gaelic football club, as well as from her old school, also attended the parish church, where pupils gave a guard of honour.
A number of children also held fiddles and tin whistles.
Vigils have been held across the island of Ireland and the world to remember Ms Murphy over the past week.
Children outside the church held photographs of Ms Murphy, bearing the words: “Fly high in the sky, our shining light.”