Ms Murphy, 23, was found dead after going for a run on the banks of the Grand Canal in Tullamore, County Offaly, at around 4pm on Wednesday 12 January.

Police have said the man who was detained is being held at the Tullamore Garda Station.

The arrest comes after Ms Murphy was remembered as a "woman who made a difference, who brought happiness and who was loved" during her funeral mass at St Brigid's Church in Mountbolus.

Funeral held for murdered primary school teacher 'who made a difference'

Bishop Tom Deenihan told mourners that Ms Murphy was "a woman who lived the short years given to her to the full, who developed her talents, who reached out to others, who made a difference, who brought happiness and who was loved".

Tens of thousands of people have attended vigils in Ireland and the UK but, while they have been remembering Ms Murphy, they have also called for more to be done to tackle violence against women and girls.

Father Michael Meade, who also addressed the mass, said Ms Murphy's parents, siblings, and boyfriend had "been robbed of your most precious gift - a gift that gave only joy and love, fun and laughter to many beyond your family".

Sky's senior Ireland correspondent David Blevins, who is in Mountbolus, said earlier: "Ashling Murphy was one of those special people who touched many hearts", adding that she had been a "very popular" primary school teacher, and a talented musician from a family well-known in the Irish traditional music community.

Pupils from Ms Murphy's class at Durrow National School formed a guard of honour and schools across Ireland observed a moment's silence at 11am.

Traditional Irish music was a theme of the service, which was also attended by Irish president Michael D Higgins, and Taoiseach Micheal Martin.