"Everyone has the right to protest, but nobody has the right to break the law," Mr Furner told reporters on Sunday.
He could not say how much the fines might be, only that they would be related to biosecurity incursions, and match "the heartbreak and concerns" they cause farmers.
Queensland farmers are already under great stress following years of drought, and more recently the floods, he said.
The Department of Agriculture and Fisheries will also form a taskforce with the state police intelligence unit to try and prevent animal activism attacks on farmers.
LNP Leader Deb Frecklington says Labor's measures don't go far enough and extremists who invade properties need to face jail time as well as serious fines.
"There has been a well organised, well-funded campaign by animal extremists that has been terrorising Queensland family businesses in regional Queensland for months," she said.
"These family businesses put food on our table and create thousands of local jobs."
Federal Agriculture Minister David Littleproud has been calling for states to impose higher fines and tougher penalties on extremists who invade farms.
He has also been calling for the Aussie Farms animal rights group to pull down a controversial map of farm locations that he says is being used as an "attack map".
The group looks set to be compelled to do so from Monday after a complaint by the National Farmers' Federation (NFF) prompted Attorney-General Christian Porter to prescribe Aussie Farms as an organisation under the Privacy Act
The Aussie Farms Map calls itself a comprehensive, interactive map of factory farms, slaughterhouses and other animal exploitation facilities across Australia.
It lists the co-ordinates of people's home farm businesses and other details, such as ABN numbers, which can be used to find more personal details about the owners.
The prescription of Aussie Farms as an organisation under the Privacy Act means it will have to comply with the provisions of the act and if found to be in breach it could face penalties of more than $400,000.
"It is completely unjust that through the publishing of their addresses, farmers and their family's should be at the mercy of these radical extremists," NFF CEO Tony Mahar said in a statement.
He thanked Mr Porter for moving promptly on the NFF's demands.