“I used to work as a bartender. These are the kinds of people that I threw out of bars all the time,” Ms Ocasio-Cortez told reporters of the incident.
Ms Greene shouted “Hey, Alexandria” twice at the congresswoman as they both left the Chamber on Wednesday, according to The Washington Post.
The freshman Representative from Georgia then shouted at the Democratic politician, asking her why she supported antifa activists and Black Lives Matter, calling them “terrorist” groups.
Ms Greene, who has already been stripped of her House committee assignments, then accused Ms Ocasio-Cortez of backing out of their planned New Green Deal debate and failing to defend her “radical socialist” views.
Ms Ocasio-Cortez did not reply or stop and just threw her hands up in the air, according to CNN.
“For me, this isn’t even about how I feel,” Ms Ocasio-Cortez later said.
“It’s that I refuse to allow young women, people of colour, people who are standing up for what they believe, to see this kind of intimidation attempts by a person who supports white supremacists in our nation’s capital.”
When asked if she felt that she was bing bullied by Ms Greene when she approached her, Ms Ocasio-Cortez said, “I mean she was certainly chasing.”
She then took to Twitter to cheekily remind her 12.7m followers to “keep generously tipping your bartenders, servers, delivery, venue, and hospitality workers.”
House Speaker Nancy Pelosi suggested on Thursday that the matter might have to be investigated by the House Ethics Committee.
“It was reported to our office what happened as members were leaving the floors yesterday, the verbal assault and abuse of our colleague, congresswoman AOC,” she said.
“It’s so beyond the pale of anything that is in keeping with bringing honour to the House or not bringing dishonour to the House.”
Ms Greene denied to reporters that she had screamed at Ms Ocasio-Cortez and said there was no need for it to go any further.
“No, she doesn’t need to file ethics violations or whatever she’s doing. That’s reacting like a child. Adults are able to debate policy.”
Ms Ocasio-Cortez is not the only member of Congress to have issues with Ms Greene.
Democratic Representative Cori Bush of Missouri moved her office away from the Georgia congresswoman following a heated exchange in January over mask wearing.
Ms Greene also faced criticism for posting an anti-transgender sign outside of her office, which is opposite the office of Representative Marie Newman, whose daughter is transgender.