Eva Resnick-Day, an activist affiliated with Greenpeace and 350 Action, two climate organizations, asked Clinton if she will "reject fossil fuel money" from her campaign.
Greenpeace USA posted video after the exchange.
Clinton, clearly aggravated by the question, responded by raising her voice to the questioner and jabbing her finger toward the woman.
"I do not have, I have money from people who work for fossil fuel companies," Clinton said. "I'm so sick. I'm so sick of the Sanders' campaign lying about me. I'm sick of it."
This is not the first time 350 Action or Greenpeace have confronted Clinton over fossil fuel donations. The groups also questioned her on the issue during an Iowa City, Iowa, town hall in December and a Dover, New Hampshire, town hall in February.
Clinton is also routinely questioned on the rope line after events by people with pointed -- and at times aggressive -- questions. Clinton is generally able to either ignore the question or answer without getting angry.
Michael Briggs, Sanders' spokesman, did not respond to Clinton accusation that the campaign is lying about her, but stood by Greenpeace's question.
"The truth is that Secretary Clinton has relied heavily on funds from lobbyists working for the oil and gas industry," Briggs said, citing a Greenpeace article
arguing that Clinton has taken donations from 57 oil, gas and coal industry lobbyists.
Nick Merrill, Clinton's spokesman, said Thursday that the Clinton campaign "has not taken a dollar from oil and gas industry PACs or corporations. The simple fact is that the Sanders campaign is misleading voters with their attacks."
The number in question, though, is donations from people who work for oil and gas companies. Under that metric, Clinton's has taken more than $300,000 from people who work for those companies, according to Greenpeace. Clinton's campaign has not received any money directly from oil and gas companies, as that would violate election law.
Merrill went on to note that "by the same metric, Bernie Sanders has taken more than $50,000 on this campaign from individuals working for oil and gas companies."
"Assuming they don't believe their own candidate is bought by the fossil fuel industry, they should stop the false attacks and do what they've claimed the campaign is about: debating the issues," Merrill concluded.
Resnick-Day, the Greenpeace questioner, said in a statement that she "was shocked and surprised at (Clinton's) reaction to my question."
"Secretary Clinton needs to listen to the people, not fossil fuel interests," Resnick-Day added.
Clinton's exchange with the activist came after a fiery event
at the State University of New York at Purchase, where Clinton called out Sanders a number of times and confronted Sanders protesters who shouted her event.
Shortly into Clinton's speech, a small group of protesters stood up and yelled, "If she wins, we lose."
Clinton looked at them and said, "Oh, I know. Bernie people came to say that."
"I have earned 9 million votes in this election. I have 1 million more votes than Donald Trump and I have 2.5 million more votes than Senator Sanders," Clinton said to cheers as the protesters were escorted out.
Clinton has personally grown more frustrated with protesters in recent days, according to aides, annoyed by the fact that many of the protesters don't come to listen to proposals but are there just to disrupt.
Republicans jumped on the video of Clinton confronting the protester. American Crossroads, an anti-Clinton super PAC, sent reporters an email with the subject line, "Hillary loses temper with Greenpeace activist." The Republican National Committee called it a "testy" exchange.