Charlie Rispoli, a 14-year veteran of the police department in the city of Gretna, described Ms Ocasio-Cortez as a “vile idiot” in a Facebook post on Friday.
Referring to her past work as a bartender, he added that the high-profile New York congresswoman “needs a round – and I don’t mean the kind she used to serve”.
Fellow officer Angelo Varisco was also fired for “liking” the post, which included a fake story making it appear that Ms Ocasio-Cortez said “we pay soldiers too much”.
The terminations were announced by Gretna police chief Arthur Lawson at a press conference on Monday afternoon.
“This incident, we feel, has been an embarrassment to our department,” he said.
“These officers have certainly acted in a manner which was unprofessional, alluding to a violent act be conducted against a sitting US [congresswoman], a member of our government.
“We are not going to tolerate that.”
The police chief said the department had contacted Facebook to see whether any other officers were involved.
Ms Ocasio-Cortez suggested that Donald Trump was to blame for the officer’s post.
“This is Trump’s goal when he uses targeted language and threatens elected officials who don’t agree with his political agenda,” she tweeted on Monday.
“It’s authoritarian behavior. The President is sowing violence. He’s creating an environment where people can get hurt and he claims plausible deniability.”
The post, which has been deleted, drew widespread condemnation, including from the mayor of Gretna, Wayne Rau, and the state’s Republican Party chairman, Tim Schneider.
It also showed Ilhan Omar of Minnesota and Ayanna Pressley of Massachusetts brandishing guns.
“Political Jihad is their game,” the post read. “If you don’t agree with their socialist ideology you’re racist.”
Ms Ocasio-Cortez was one of four Democrat congresswoman who were told by Mr Trump to “go back and help fix the totally broken and crime infested places from which they came.”
Additional reporting by agencies