The shooting occurred at a home near Omeath, County Louth, close to the border with Northern Ireland, police said.
"Two people (adult males) have been fatally injured and one adult female seriously injured as a result of this incident," a statement from national police service An Garda Siochana said.
"We can confirm that one of the deceased was an on duty member of An Garda Siochana."
The police officer was responding a call about a domestic disturbance, Irish media reported.
Gerry Adams, who represents the Louth constituency as a lawmaker and is the president of the left-wing nationalist party Sinn Fein, said he was "shocked" at the news.
"My thoughts and sympathies are with the families of those who have died," Adams said in a statement.