Jones also hurled other attacks at Rubio, including calling the Florida senator a "little frat boy", "snake-like" and a "gangster thug".
Rubio was talking to reporters outside a hearing on foreign influence in social media when Jones started shouting questions at Rubio, at one point putting his hand on Rubio's shoulder.
"Don't touch me again, man", said Rubio.
When Rubio told Jones, "Don't touch me again, man", Jones taunted, "Well sure, I just patted you nicely".
"Oh, he'll beat me up?"
Last month, Twitter banned Jones and Infowars for seven days, citing tweets that it said violated the company's rules against abusive behavior, which state that a user may not engage in targeted harassment of someone or incite other people to do so.
"Who's this guy, why are you platforming him?"
The suspension means Jones won't be able to create new accounts on Twitter or take over any existing ones, the company said. "Rubio just threatened me physically".
Twitter CEO Jack Dorsey and Facebook Chief Operating Officer Sheryl Sandberg testified before the Senate Intelligence Committee Wednesday about their companies' alleged anti-conservative bias and foreign governments manipulating social media platforms to influence USA politics.
Jones has a right to free speech, but nothing in the Constitution guarantees him access to privately-owned platforms to spread that speech. "What about the Democrats purging conservatives", Jones said, cutting off Rubio's answer to a journalist with CNBC.
Jones was previously suspended by the service for a week.
Following the proceedings, Jones stood outside heckling Rubio as he interviewed with the press. "As the president says, it is a witch hunt, but it's beyond a witch hunt", Jones said earlier Wednesday.
Rubio then moved away from the reporters, saying "you guys can talk to this clown".
Jones is now being sued in Texas by two Sandy Hook parents, seeking at least $1 million (£0.77 million), claiming that they have been the subject of harassment driven by his programs. There are certainly plenty of censorious voices on the left looking for any excuse to silence people they disagree with and Alex Jones could be the camel's nose under the tent.