The commercial, by Meat & Livestock Australia (MLA), was released on Saturday and has since gone viral.
It shows a SWAT team "saving stranded Aussies" abroad from missing a barbeque on the country's national day.
The Advertising Standards Bureau (ASB) said it has received about 250 complaints, mostly from vegans.
ASB said it was also reviewing complaints of violence, and discrimination against Indigenous Australians.
The campaign has been accused of cultural insensitivity for using the slogan "Operation Boomerang" - an Indigenous term - to mark Australia Day.
The national day commemorates the arrival of the first Europeans in the country but is seen by many Indigenous Australians as a day of mourning.
In one scene in the advert, a SWAT team smashes into the home of a man in New York saying "C'mon mate, in a few hours you'll be eating lamb on the beach", to which the the bearded man responds: "But I'm a vegan now...".
The ad later cuts to a shot of a flamethrower-wielding SWAT officer burning a bowl of kale on the vegan's table.
Meat & Livestock Australia said the ad was "tongue in cheek".
"Consumers are free to make up their own minds in relation to lifestyle choices, including what they eat. We appreciate that not all Australians eat lamb," group marketing manager for MLA Andrew Howie said in a statement.
"MLA is also aware of some complaints about the use of the word "boomerang" in the advertisement. It is not our intention to cause any offense through the use of this term which is used to symbolise Australians returning home for Australia Day."
Extracts of the complaints will be published on the Advertising Standards Bureau website after its next board meeting in about two weeks time, an ASB spokesperson said.
An action movie-style advertisement campaign to promote Australian lamb has angered vegans who call it "discriminatory".