Ashling Murphy, from Tullamore in Ireland’s County Offaly, was attacked on Wednesday afternoon at around 4pm while jogging along the banks of a canal at Cappincur.
A 40-year-old man has been arrested by the gardai and is being detained at Tullamore Garda station.
Superintendent Eamonn Curley told reporters on Thursday: “At this stage, there is no information that the victim and her killer were known to each other.
“From our enquiries we have carried out, we believe this crime was committed by one male who acted alone.”
Police are appealing for help from the public for information about the case which has shocked the country, saying they are keeping an “open mind”.
They have vowed that “no stone will be left unturned” in bringing her killer to justice.
Declan Harvey, Fianna Fail councillor for the area, said: “I want to extend my sympathies to Ashling’s father, mother and all her extended family.
“I am devastated. I couldn’t sleep last night thinking of it all because it is a place I go all the time.
“She went there jogging, she does it regularly. I am lost for words.”
Justice Minister Helen McEntee tweeted: “My thoughts tonight are with the family of the young woman killed in a truly shocking crime, with her friends and with her community.”
Further Education Minister Simon Harris said: “A young woman, simply out for a run in the afternoon and brutally killed.
“Thinking of her and her family and community tonight and their unimaginable pain. We must all act to end violence against women.
“We all have a responsibility.”
Over 50 gardai are working on the investigation, and they have asked anyone in the area before 4pm on Wednesday to make contact with them.