The suspension comes pending the outcome of an investigation by the charity commission into the finance of the association.
The investigation "is focussed on addressing concerns about the governance and financial controls".
All five of the association's officers deny any wrongdoing.
The charity, which receives more than £100,000 in funding each year, organises events and excursions for former police officers injured on duty.
Membership is open to ex-RUC and PSNI officers. In recent years it has organised trips to London, Dublin, Cork , Poland and the K Club in County Kildare.
An apparent conflict of interest, potential misconduct, not following financial procedures, misleading members of the charity, and non-compliance with funding conditions are some of the claims being examined by investigators in relation to the suspended chief executive, Elaine Hampton.
The commission is also looking at whether or not the charity may have applied for double funding for some trips.
Ms Hampton said she did not wish to comment for fear of prejudicing an appeal she has lodged against her suspension.
It is understood she denies "any financial irregularities of any description" at the DPOANI, or indeed any wrong-doing.
The association receives funding from the public purse, including income from the Northern Ireland Police Fund, the Community Relations Council and OFMDFM's Victims and Survivors Service, to help pay for its activities and trips.
It also receives donations including one of almost £20,000 a year from the Greater Manchester Police.
The Northern Ireland Police Fund, which is funded by the Department of Justice, confirmed it has frozen any grants to the association pending the outcome of the charity commission's inquiry.
As well as the chief executive, Elaine Hampton, four other trustees, chairman Billy Allen QGM, audit committee member Robert Crawford, director Gordon Knowles MBE and former assistant treasurer Stephen McAlister, have been suspended pending the outcome of the commission's investigation.
It is understood all five are appealing the commission's decision.
Billy Allen is accused of not following financial procedures. Mr Allen declined to be interviewed saying he did not want to prejudice the outcome of his appeal. It is understood he strongly denies any wrongdoing.
After first suspending Robert Crawford, the charity commission is now trying to remove him from the charity altogether.
He is accused of mismanagement of the audit committee. Mr Crawford declined to be interviewed, also saying he did not want to prejudice his appeal against the suspension.  It is understood he believes he did nothing wrong.
As a consequence of the commission's actions, Mr Crawford has now been suspended from his post as a senior civil servant at the Department for Regional Development.
It Is understood the commission is also examining concerns that some people not eligible for membership of the charity benefited from what it said could be "excessively lavish expenditure of public money", by taking part in a visit to the exclusive five star K Club golf resort in County Kildare in March. It is believed accommodation and meals for the three-day trip cost around £12,000.
According to the commission, suspended board member Stephen McAlister,  who attended the trip to the K Club, was "not eligible under the charity terms and conditions for DPOANI membership".
Mr McAlister, an ex-RUC reservist and now leading member of the Orange Order, said his health had deteriorated since he was removed as a trustee.  He said he was entitled to be a member of the association on the basis that he had been shot in the face in an INLA gun attack in Belfast in 1979.
He said:  "The membership criteria for the association changed after I became a member.
"We have found the records which would override what they (the charity commission) are saying.  They are also looking at something to do with double funding which is rubbish.
"There are no financial irregularities whatsoever in the organisation and I think they (the charity commission) are on a fishing expedition."
Ex-RUC officer, Gordon Knowles, who has also been suspended, was shot seven times in an ambush on Rosslea police station in County Fermanagh in 1955.  He too has been told he does not qualify to be a member of the DPOANI.
Commenting on his suspension, Mr Knowles said: "I am completely gutted.  Absolutely gutted. I don't know what I have done.  My whole policy was to help my fellow man (by) being in the DPOANI."
The accountancy firm Harbinson Mulholland Accountants has been appointed interim managers of the DPOANI.  Records at Companies House show the charity has around £177,000 cash in the bank.
The chief executive and four trustees of the NI Disabled Police Officers Association (DPOANI) have been suspended.