Richardson City Councilman Scott Dunn replied to Ms Ocasio-Cortez on Twitter with the offending remarks, according to screenshots of the tweet that circulated online last week.
“The embarrassment is to have bimbos like you with nothing between your ear,” Mr Dunn wrote.
It's unclear to which of the congresswoman's tweets he was responding. As of Saturday morning, Mr Dunn's Twitter account was deactivated.
Mr Dunn later said he was trying to defend Donald Trump after the State of the Union address, according to the Dallas Morning News.
The day after the speech, Ms Ocasio-Cortez called the event an “embarrassment” after some criticised her for not applauding Trump and looking “sullen” in the audience.
In a Facebook post on Friday, Mr Dunn apologised for his Twitter reply to Ms Ocasio-Cortez, according to the New York Daily News. The post was no longer publicly visible as of Saturday morning.
“The words I used were offensive,” Mr Dunn reportedly wrote. “I am responsible for my own words and actions. I apologise to anyone who finds what I said offensive.”
Mr Dunn did not immediately respond to a request from the Washington Post for comment on Saturday.
Even after Mr Dunn's Twitter account was deactivated, screenshots of his tweet were circulated on social media, prompting a few calls for him to resign.
Mauri Long, a candidate for Richardson City Council, said she found the tweet “inappropriate, demeaning and divisive”.
“As one of only two women running for City Council, I find this sort of locker room talk disturbing and personally offensive,” Ms Long wrote in a post on her campaign's Facebook page.
“This type of caustic rhetoric by an elected representative of our great city is not reflective of our own values.”
Amir Omar, a former Richardson City Council member, also condemned Mr Dunn's remarks as unbecoming of an elected official.
“I really don't care what political team you root for and whether you like one representative or another,” Mr Omar wrote.
“I don't even care that although you are representing a city in a non-partisan role, you can't hold your tongue out of basic decorum.
"What I do care about is that you are so tone deaf that you don't realise that using sexist terms like this one reflects badly on our city.”
On Friday, Richardson Mayor Paul Voelker said he was “extremely disappointed and embarrassed” by Mr Dunn's comments and had since talked to the council member.
“While I certainly respect councilman Dunn's, or any citizen's, right to freely express his or her opinion on any issue of public concern, I also believe that Richardson's values are best upheld when we engage in civic discourse that is civil in tone, respectful of others and designed to produce constructive outcomes for the betterment of our community,” Mr Voelker said in a statement.
“Even when we disagree about important political and social issues, we shouldn't resort to name-calling,” the mayor added.
Ms Ocasio-Cortez upset long-time congressman Joseph Crowley in their Democratic primary race last year, and quickly became a popular target of the right even before she took office. Republican lawmakers and pundits have mocked everything from Ms Ocasio-Cortez's appearance to her background.
There are new examples all the time. Republicans Ed Rollins and Rush Limbaugh recently dismissed Ms Ocasio-Cortez as a “little girl” and “some young uppity.”
The Washington Examiner's Eddie Scarry tweeted a photo of her in November and wrote that she doesn't “look like a girl who struggles.” The Daily Caller promoted what it described as a possible “nude selfie” of her last week before walking back its headline.
In return, Ms Ocasio-Cortez has frequently clapped back at her critics online and in interviews. She did not, however, appear to respond to Mr Dunn's “bimbos” tweet.
Mr Dunn has served on the city council in Richardson, a Dallas suburb, since 2011, according to his bio.
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