Hours later, Clinton's former campaign manager, Patti Solis Doyle, said it was "disappointing" that Clinton hadn't yet condemned Weinstein's purported behavior.
"Any leader should condemn this," Kaine told CNN's Alisyn Camerota in an interview on "New Day," referring to the bombshell allegations of sexual harassment by the disgraced Hollywood executive. "These allegations are low-life behavior."
The Virginia Democrat ran alongside Clinton on the Democratic presidential ticket during the 2016 election. Weinstein was a frequent Democratic donor who gave thousands of dollars to their campaign for the White House.
While many Democrats have sent Weinstein's donations to charity, several prominent Democrats -- including former Presidents Barack Obama and Bill Clinton, as well as Hillary Clinton -- have not publicly addressed the accusations.
Camerota noted that Weinstein donated more than $30,000 to the Clinton campaign. She pressed him on whether the money should be returned.
"Well, the campaign is over," Kaine replied.
"Here's what's happening: You've got to call out bad behavior," he continued. "Anybody who sexually harasses somebody or anybody who uses their position of power, especially to coerce or intimidate anybody, that's low-life behavior and that's unacceptable ... I think a number of folks he has given to in this campaign cycle are returning those funds."
He added, "I haven't asked him for anything and he hasn't given me anything."
When asked why Clinton has remained silent about Weinstein, Kaine responded he's "nobody's press secretary."
"I'm a US senator, and I'm telling you that sexual harassment is unacceptable," he said. "Hillary Clinton speaks out against sexual harassment often and I'm sure she'll have a word to say when the time is right for her."
The recent report in The New York Times
cataloged accusations of sexual harassment against the filmmaker that spanned three decades. Three days after the report, Weinstein was fired by the company he co-founded.
Longtime Clinton aides have been confused by the former secretary of state's silence on the issue, questioning -- in private -- why she has not weighed in at all.
"Personally it is, it is disappointing she hasn't come out and condemned Harvey Weinstein," Solis Doyle told CNN's Poppy Harlow in an interview on "CNN Newsroom" Tuesday morning.
Weinstein has long been a Clinton donor with ties to the political family. Weinstein was one of many from Hollywood who donated to Bill Clinton's legal defense fund in the 1990s, a Washington Post report from the time stated. More recently, the Clintons rented a home next to Weinstein in the Hamptons in 2015, and Weinstein served as a connector between Hollywood stars and Clinton's 2016 campaign.