Officers from the Garda’s Special Detective Unit made the arrests this morning under the Offence Against the State Act.
The men, who are both in their 40s, are being questioned at a Dublin garda station.
The improvised device was found under the PSNI officer’s car at Shandon Park Golf Club on Saturday, June 1.
A tournament, which was being held at the golf club, was cancelled and around 70 people were evacuated.
Detective Superintendent Sean Wright of the PSNI’s Terrorist Investigation Unit said at the time that police believed dissident republicans were behind the “attempted murder”.
Detectives believe the device was attached at the officer’s car parked at his nearby home in east Belfast hours earlier following a scouting operation by two cars.
One of the cars had a Dublin registration plate.
Speaking today after the arrests in Dublin, Detective Superintendent Sean Wright said: “I welcome this development and it demonstrates the excellent working relationship between PSNI and AGS.
“The arrests should send a clear message to those involved in terrorist activity that the border does not provide an escape route.
“Our two police services work collaboratively on a daily basis, sharing knowledge and information, to ensure that there is no hiding place for criminals or terrorists.
“My detectives continue to investigate this reckless attack on a public servant and we have considerable support from our AGS colleagues.
“If you have information about the incident or you suspect that someone you know is a member of a dissident republican group, then contact detectives on 101 or let us know through the confidential Crimestoppers number on 0800 555 111.”