A damaged car was later found abandoned - writes herald.ie
One of the graves is that of local respected Superintendent Denis Hogan, who died in 1984.
His wife Olive, who died two years ago, is also buried in the same plot.
Their son Damian, who is a serving Garda Sergeant, condemned the actions of whoever was responsible for the vandalism.
"This is a despicable thing to do in sacred ground and extremely distressing for the families involved," he said.
"The two graves are beside each other. The plinth on my own parents' plot has been badly damaged, but the damage to the second grave is shocking," he added.
The second grave is that of John Joseph Thornton, who passed away in the mid 1980s.
"That headstone is completely smashed and lying in several pieces on the grave. It is awful to see it. We really can't understand why anyone would do something like this," said Sgt Hogan.
The fact that the two men had served in An Garda Siochana is inscribed into the headstones, and gardai are trying to establish whether the incident deliberately targeted the graves of former officers or was more random in nature.
"The people left hurting are the families of the deceased who are still mourning," added Sgt Hogan.
"This vandalism shows a total lack of respect for the dead and the living.
"The people who did this need to be held accountable and I would urge anyone who knows anything to contact the gardai in confidence."
The cemetery has been used by some members of the community for antisocial activity and drinking in the past, but this type of vandalism has never been reported at the location before now.
Some families living nearby reported the vandalism and called gardai.
Read more news of Dublin on our site.