Garda said on Wednesday that a second man, aged in his 30s, has been arrested and is being questioned in relation to the potential withholding of information.
The man is being held at a garda station in the east of the country.
Another man remains in custody on suspicion of murdering Ms Murphy in Tullamore, Co Offaly.
The man, who is aged in his 30s, was arrested on Tuesday in Co Offaly.
Irish police said the man is still being questioned at Tullamore Garda station.
The arrest was made after police renewed an appeal for information, saying “significant progress” had been made with their investigation.
The body of Ms Murphy, a talented musician and teacher, was found on the banks of the Grand Canal in Tullamore last Wednesday.
Large crowds gathered in the village of Mountbolus and outside St Brigid’s Church where her funeral was held on Tuesday.
Mourners included Irish president Michael D Higgins and Irish premier Micheal Martin.
Vigils have been held across Ireland and the world to remember Ms Murphy and to call for a change in tackling gender-based violence.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in