The bank is the biggest backer of the high profile Dutch Rabobank team, with total sponsorship worth 15 million euros a year in a cycling-mad nation with as many bikes as people.
The decision shows the damage being done to cycling after the US Anti-Doping Agency said Armstrong had taken part in and organised a sophisticated doping scheme on his way to success.
"We are no longer convinced that the international professional world of cycling can make this a clean and fair sport. We are not confident that this will change for the better in the foreseeable future," Bert Bruggink, a Rabobank board member, said in a statement.
"The USADA report was the final straw," he added later at a news conference televised live in the Netherlands.
"The international sport of cycling is not only sick, the sickness goes up to the highest levels," he said.
Sportswear company Nike and brewing group Anheuser-Busch dropped their sponsorship of Armstrong this week, and the sport must show it can tackle doping effectively to prevent more of its backers from quitting.
The International Cycling Union, the sport's governing body, has yet to rule on the USADA's report into Armstrong and has been criticised for dragging its feet.
"Despite inevitable and sometimes painful consequences, the UCI reaffirms its commitment to the fight against doping and full transparency about potential anti-doping rule violations," the Swiss-based UCI said on Friday.
Armstrong, a 41-year-old cancer survivor, has always denied taking banned substances but has decided not to challenge the USADA charges.
The Rabobank decision was criticised by British cyclist David Millar, an ex-doper turned anti-doping campaigner, who tweeted: "Dear Rabobank, you were part of the problem. How dare you walk away from your young clean guys who are part of the solution. Sickening."
Rabobank declined to comment on Millar's tweet. But its decision is a blow to Dutch riders including Marianne Vos, an Olympic gold medallist, and her team's preparations for the 2016 Games.
Bruggink said Rabobank would do "everything we can to support her 2016 Olympic ambitions" but did not elaborate.
American rider Levi Leipheimer, who rode for Rabobank between 2002 and 2004, was sacked this week by the Quick-Step Cycling Team after admitting to the USADA investigation that he took banned substances.
Leipheimer, 38, was one of 11 former team mates to testify against Armstrong.
Another sponsor, SKINS, which is a partner of the Rabobank team, said on Thursday it would reconsider its association with the sport if the UCI failed to act on doping.
SKINS Chief Executive Jaimie Fuller warned the commercial fall-out could be worse than the damage suffered by a doping scandal centred on the Festina team that hit the Tour de France in 1998.
Cycling has attracted a new generation of sponsors in recent years who stress their commitment to clean competition.
Huib Kloosterhuis, the head of the Dutch Cycling Union, said it was "a black day for us and cycling in the Netherlands" and it would be hard to replace Rabobank in the current environment.
The sport increasingly appeals to affluent fortysomethings who want to stay active for longer - earning it the nickname "the new golf" and boosting its commercial appeal.
British team Sky, sponsored by pay-TV company BSkyB, said this week it would sack team members unless they signed a document saying they had never doped. Sky rider Bradley Wiggins this year became the first Briton to win the Tour.
The Rabobank cycling team, which has taken part in every single Tour de France since 1984, said it regretted but understood the bank's decision.
"We've been cycling for 17 years now with the name Rabobank proudly on our shirts, and it hurts that going forward we'll have to do without that name," it said.
Its top riders are Dutchman Robert Gesink, this year's Tour of California winner, and Spaniard Luis Leon Sanchez, winner of four Tour de France stages.