It happened on the M50 motorway between the  Blanchardstown and Finglas junctions.
In a tweet, the Football Association of Ireland said: "The ROI mgmt team were involved in collision on M50 earlier. Vehicle was rear ended in traffic."
It said they had returned to their hotel and were seen by the team doctor.
The FAI have said that O'Neill and Keane were accompanied by coaches Seamus McDonagh, Steve Guppy and Steve Walford at the time of the accident.
Nobody involved in the incident was seriously injured.
Ireland face Scotland at the Aviva Stadium on Saturday evening in a crucial Euro 2016 qualifier.
The Republic of Ireland management team, including manager Martin O'Neill and his assistant Roy Keane, have been involved in a car crash in Dublin.