The online clip, which has been widely shared, references the woman going to “Mauritius on her honeymoon”.
Those singing go on to mock her death in the hotel room on her honeymoon and reference the woman’s father, the multiple All-Ireland Senior Football Championship-winning Gaelic football manager Mickey Harte.
The video shows a group of men in a room of dozens of people, drinking, laughing, and chanting.
While it has not yet been verified where the scenes in the video took place, it is understood it occurred during the Centenary celebrations, with Orange Order banners in the background and Union flag bunting.
The DUP leader Jeffrey Donaldson described it as “vile”, adding that it is “plain wrong and is deeply hurtful to the family of Michaela McAreavey”.
Arlene Foster added the footage was “just so wrong and hateful” and sent her love to Mrs McAreavey’s families.
Sinn Fein MP Michelle Gildernew expressed her outrage online, with the Fermanagh and South Tyrone representative confirming she has contacted the PSNI.
“Thank you to everyone who reported this to me tonight,” she wrote.
“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.”
Ulster Unionist Party leader Doug Beattie described the video as “absolutely abhorrent, disgusting and shameful”.
South Belfast Alliance Party MLA Kate Nicholl said the scenes had shocked her.
"The hatred displayed in the video of men singing & laughing about the horrific murder of a young woman is incompressible. How her poor family must feel. I have reported to the police,” she said.
Sinn Fein’s Linda Dillon added: “Wouldn’t dream of reposting the video doing the rounds because I have one beautiful wee girl and if that was my daughter my heart would be broken. My deepest thoughts are with the family. I am forever grateful my child is not capable of that kind of hatred.”
Mid Ulster MLA Patsy McGlone called the scenes “about as base in humanity as you can go – singing and laughing about the murder of an innocent young woman.”
SDLP Mid Ulster councillor Malachy Quinn added his condemnation, writing: “I was sent this video. I haven't the words to describe my anger at a song being sung mocking the murder of Michaela McArevey, never mind it being sung at a ‘Centenary Event’.
“This is beyond reprehensible. Those involved should be bloody ashamed.
I also can't describe the anger in my own community about this video.”
Mrs McAreavey, 27, was strangled in her room at the Legends Hotel in Mauritius on January 10, 2011.
The teacher, who had married husband John 10 days earlier, was attacked after she returned to her room alone and was disturbed a burglary.
No-one has been convicted of murdering the daughter of former Tyrone football manager Harte.