"Authorities in five countries including the Netherlands, Serbia, Croatia and Canada, with support from Police Scotland and Europol, targeted six members of the crime group behind webstresser.org," the NCA said in a statement.
Cyber-criminals used the website's services, which could be rented for as little as $14.99, to launch so-called distributed denial of service (DDOS) attacks, which swamp targets with traffic and disable their IT systems.
British police searched an address in Bradford, northern England, and seized a number of items, while Dutch police, with assistance from Germany and the United States, seized servers and took down the website,Presstv reported .
Police believe an individual linked to the address used the site, the world's largest illegal DDOS seller, to hit seven of Britain's biggest banks in November, forcing them to reduce operations.
"Stressers" services give users the ability to stress-test the resilience of servers, causing disruption to the target.
"A significant criminal website has been shut down and the sophisticated crime group behind it stopped as a result of an international investigation," said the NCA's Jo Goodall.
"The arrests made over the past two days show that the internet does not provide bullet-proof anonymity to offenders and we expect to identify further suspects linked to the site in the coming weeks and months as we examine the evidence we have gathered," she added.
Dutch National Police's Gert Ras was quoted in the NCA statement as saying that the operation had "made an unprecedented impact on DDOS cyber-crime."
"This is a warning to all wannabe DDOS-ers... we will identify you, bring you to court and facilitate that you will be held liable by the victims for the huge damage you cause."