Two suspects were arrested near the Dublin airport, The Irish Times reported. Both were believed to be Dublin residents.
The dead officer, Detective Adrian Donoghue, and Detective Joseph Ryan were on escort duty, police said. They apparently interrupted an attempted robbery of the Lordship Credit Union in Dundalk at about 9:30 p.m.
Ryan was not injured, police in Dundalk said. A car left the scene immediately after the shooting and was believed to be carrying four people.
Donoghue, said to be in his late 30s, was married to a police officer and had two brothers on the force, police said.
"He was on duty in the service of his country and it looks like he could have paid the ultimate price," a senior officer said.
"It doesn't look like it's going to be a good night for An Garda Síochana (the Irish police)."