Ms Ocasio Cortez, representative for New York's 14th congressional district, responded to a tweet showing that Project Veritas received half a million dollars in Covid bailout funds.
Project Veritas is a far-right activist group, which says it uses undercover techniques to reveal so-called liberal bias and corruption.
Responding to the decision, Mr Ocasio-Cortez wrote: "Black-owned small businesses were widely shut out from accessing PPP loans, yet right-wing disinfo org PV took half a million in public money while decrying direct federal assistance as 'radical socialism.'
"Republicanism in a nutshell."
Mr Rubio hit back at the congresswoman's remarks, saying that Republicans and Democrats had "worked together" to help save the jobs of "55 million Americans through PPP".
"Work more, tweet less & one day you too can make a difference," he added in response to Ms Ocasio-Cortez's origial tweet.
As the Covid-19 pandemic pushes many hospitals across the country to breaking point, the Twitter spat then seemingly descended into a row over which lawmaker had the busier week.
"Yesterday I recruited 5,000 volunteers to train and tutor kids in my community who are struggling with remote learning, and that was after investigating the Treasury Secretary's rationale for stopping CARES Act funding and voting on House legislation," Ms Ocasio-Cortez fired back.
She then asked the GOP senator: "What did you do?"
After apologising for his "late response", Mr Rubio said he had been helping his constituents.
He wrote: "Was busy this week helping a Floridian get travel documents to see his dying sister, a high schooler whose mother died get SSI benefits, a specialist for a child with a crazy Obamacare deductible & negotiating Intelligence bill & another round of PPP."
Mr Rubio is the chairman of the Senate Small Business and Entrepreneurship Committee, which developed the PPP loan scheme.
It provides small businesses with federal relief during Capitol Hill shutdowns.