No details have emerged on what sports the bets were placed.
Athletes and officials placing bets at the Olympic Games is not illegal, but is against the rules of the International Olympics Council (IOC).
Belfast boxers Paddy Barnes and Michael Conlan have told the BBC that they are not the boxers involved.
The OCI said the two boxers at the centre of the investigation have been spoken to about "inappropriate betting activity".
"The matter is still under review so there will be no further comment at this stage," it said in a statement.
The Irish Athletic Boxing Association (IABA) said it had not received any notification from the OCI regarding the allegations of inappropriate betting activity but understands that the matter is being reviewed.
In a statement, it said any form of gambling was prohibited for athletes taking part in the Olympics and that it would be "very disappointed" if members of the team had broken the rules.
The incident is the latest in a series of controversies to hit the Irish Olympic team.
Boxer Michael O'Reilly was prevented from competing after failing a drugs test before the games. He said he unintentionally took a supplement that may have contained a banned substance.
Former OCI president Pat Hickey is being held in a Rio prison after being arrested in connection with the alleged illegal sale of Olympic tickets. He denies any wrongdoing.
Two Irish boxers have been investigated over betting at Rio 2016, the Olympic Council of Ireland (OCI) has confirmed.