Charles Rispoli wrote that the Democrat needed "a round", which was then "liked" by a fellow officer.
The police chief of Gretna said it was "an embarrassment to our department".
It comes days after President Donald Trump's comments about Ms Ocasio-Cortez and three of her colleagues in Congress that were widely derided as racist.
His tweets telling four congresswomen - all US citizens - to "go back" where they came from sparked an outcry from Democrats, as well as condemnation from some Republicans.
Charles Rispoli of the Gretna police department in Louisiana was responding to a post by a satirical news website that falsely suggested Ms Ocasio-Cortez believed US troops were overpaid.
"This vile idiot needs a round...and I don't mean the kind she used to serve," he wrote.
Ms Ocasio-Cortez, 29, worked as a waitress and bartender before stunning the political world last year by defeating veteran Joe Crowley in their party's congressional primary in New York City.
Gretna Police Chief Arthur Lawson told reporters that both Charles Rispoli and a fellow officer who "liked" the post, Angelo Varisco, had been fired.
"These officers acted in a manner which was unprofessional, alluding to a violent act to be conducted a sitting U.S. congresswoman," Mr Lawson said.
Both men were found to have violated the police department's social media rules, on which they had been trained.
Fallout from Trump's tweets
The US president caused international outrage last week over a series of tweets about Ms Ocasio-Cortez and fellow first-term, ethnic minority lawmakers Rashida Tlaib, Ilhan Omar and Ayanna Pressley.
Mr Trump said the women "originally came from countries whose governments are a complete and total catastrophe" and should "go back".
The president did not explicitly name the women in his initial Twitter tirade, but the context made a clear link to the four Democratic congresswomen, who are known as The Squad.
Ms Ocasio-Cortez tweeted: "He's simply an impulsive racist, one who leaves his party scrambling to excuse bigotry and scam the country."
At a rally just days later, Mr Trump criticised Ms Omar, which was followed by calls of "send her back" echoing around the arena. The president later said he disagreed with the chants.
But he later continued his tirade, calling the congresswomen "a very racist group of troublemakers" who were not "capable of loving our country".
An Illinois Republican group was forced to apologise on Monday after a post appeared on its Facebook page showing images of the four congresswomen, referring to them as the "Jihad Squad".
Ms Omar and Ms Tlaib are the first two Muslim women in Congress.
A Virginia pastor has since sparked controversy for putting up a sign at his church saying "America: Love or Leave It".
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