Politicians from across Northern Ireland have united to condemn the video, while several said they would be referring the clip to the PSNI.
A spokesperson for the Orange Order called it “utterly abhorrent”.
Mrs McAreavey, 27, was strangled in her room at the Legends Hotel in Mauritius on January 10 2011.
It’s so sick and shameful. Thinking about the Harte family who’ve been so strong and dignified. They do not deserve this
Justin McNulty, SDLP MLA
The teacher, who had married husband John 10 days earlier, was attacked after she returned to her room alone and disturbed a burglary.
No-one has been convicted of murdering the daughter of Gaelic football manager Mickey Harte.
In the social media video a number of men appear to sing about the murder of Mrs McAreavey.
A Grand Orange Lodge of Ireland spokesperson said: “The video currently circulating on social media relating to the murder of Michaela McAreavey is utterly abhorrent and the Orange Institution condemns the content without reservation.
“The behaviour of those involved and their actions have no place in our society and certainly do not reflect the ethos of our organisation.
“The Grand Orange Lodge of Ireland has instigated an inquiry into the incident and if any of those involved are found to be members of the institution, they will face disciplinary proceedings.”
Sinn Fein MP for Fermanagh and South Tyrone Michelle Gildernew tweeted: “Thank you to everyone who reported this to me tonight.
“A beautiful young woman was murdered on honeymoon & this is how loyalists ‘celebrate’ the Queen’s jubilee.
“I have reported this to the PSNI & will be taking further action.”
SDLP MLA Justin McNulty wrote on social media: “Fist pumping, table banging, clapping, laughing, jeering – singing a song about the shocking murder of one of the most beautiful people you could ever meet.
“It’s so sick and shameful. Thinking about the Harte family who’ve been so strong and dignified. They do not deserve this.”
DUP MLA Jonathan Buckley said: “This is wrong on so many levels.
“I remember the utter devastation felt by all following the tragic killing of Michaela McAreavey.
“My thoughts are with the McAreavey and Harte family circles and I condemn this vile video.”
Ulster Unionist leader Doug Beattie said on Twitter that the video was “absolutely abhorrent, disgusting and shameful”.
UUP deputy leader Robbie Butler said he was “absolutely appalled and disgusted” at the video.
TUV leader Jim Allister tweeted: “The video glorying in the murder of Michaela McAreavey is beyond disgusting, bringing shame and dishonour on all associated with such loathsome behaviour.”
A PSNI spokesperson said: “Police are aware of the video posted online and are examining the content to determine if any offences may have been committed.”
In a statement on Friday afternoon, Linfield Football Club confirmed that it had contacted a girls’ academy coach in relation to the video.
The club said that his “voluntary association with the club has been terminated with immediate effect”.
The statement called the video “offensive, sickening and deeply hurtful”.
“Linfield FC apologises to the Harte/McAreavey families for the hurt that has been caused to them by the offensive actions of one of our now former coaches.
“Linfield FC is totally opposed to sectarianism, bigotry, racism, prejudice and all forms of discriminatory behaviour and there can be no place within this club for any of these forms of offensive and unacceptable behaviour.”
Construction supplies company Norman Emerson Group also issued a statement to say it was looking into the alleged involvement of an employee and said that a “full and thorough internal investigation” was under way.
“We will not tolerate or condone sectarianism, bigotry, or intimidation in any form from anyone employed by us.”