The petition is hosted on campaigning website Avaaz.com and claims the fee, introduced in January 2013, is not just unfair but also illegal.
Under the system, every home must pay a flat monthly rate of €17.98 regardless of whether it has a TV or radio.
"This amounts to a tax which is banned by the constitution for good reasons," the petition said. "Every person has the natural right not to be forced to finance companies."
It argues the state broadcasters should instead be funded by "Pay-TV" or adverts rather than a compulsory levy on all households.
The petition, uploaded to the site at the beginning of December 2013, has a target of 1,000,000 signatures.
The so-called Rundfunkbeitrag (broadcasting contribution) brought in last year has also been attacked by large retail chains whose overhead costs are set to increase.
Deaf and blind people, who were previously exempt from the licence fee, can find themselves paying under the new rules.
But households of multiple people with their own TVs, computers and radios will benefit from the system, as the previous rules stacked up charges for each occupant's devices.
The flat-fee model is meant to take into account media being shared across platforms and simplify paying into the state-funded broadcasters by merging the contributions for individual devices into one bill.
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