According to the complaint, filed on Monday with Sweden's Finansinspektionen (FI), banks in Sweden have broken the law by denying Swedes the ability to make donations to the whistle blower website.
"The blockade is a serious threat to freedom of speech and expression," Erik Lönroth of the Pirate Party said in a statement.
"It shouldn't be up to a specific payment service to decide what sort of activities are appropriate and deserve the ability to receive financial support."
Starting in December 2010, Visa, Mastercard, PayPal, and other payment service providers stopped processing payments to WikiLeaks, making it difficult for would-be donors to support the whistleblower website.
WikiLeaks claims it has lost 95 percent of its revenue due to the blockade.
The Pirate Party complaint alleges that since banks in Sweden utilize the payment services behind the WikiLeaks blockade, they are breaking Swedish laws by denying Swedes the ability to donate to WikiLeaks.
According to the Pirate Party, Sweden's banks are "actively participating in blocking transactions without a legitimate reason".
"It's frightening that we're all forced to live by the morals of the American Bible Belt by the companies that handle our payments," Pirate Party head Anna Troberg said in a statement.
"These companies happily deliver funds to the Ku Klux Klan, but not to WikiLeaks and other companies they view as immoral."
As the banks singled out by the Pirate Party – Danske Bank in Sweden, Swedbank, Handelsbanken, Nordea, and SEB – all fall under the purview of Finansinspektionen, the party hopes the agency will take action to probe whether the banks are in violation of the law by failing to carry out transactions on behalf of their customers.
Speaking with the Dagens Nyheter (DN) newspaper, the head of Finansinspektionens payments division, Johan Terfelt, confirmed the agency had received the complaint and would assess whether there was reason to act.
"The law says that if there aren't legal grounds for denying a payment, it should be carried out," he said.
Examples of legal grounds included being unable to identify the recipient of the payment or if there are reasons to suspect the money may go to finance terrorism.
However, Terfelt refused to elaborate on exactly what responsibility Swedish banks had when a payment service provider like Visa orMastercard decides to block payments.