No, the magnet â even the small ones on the back of a piece of paper or card â cannot be recycled along with the card or paper itâs attached to. For example,
Recyclopaedia - Magnets | ACT Government
Magnets such as fridge magnets and other small household magnets are not recyclable in ACT recycling bins.
Any plastic magnets that make it to the recycling processing centres might be picked up by the large magnets used for extracting steel items such as cans, but theyâd simply be tossed out from there because they canât be recycled with the metal. Similarly if they get past the steel-catcher to the manual sorting section. Theyâd just be tossed out, like other items that canât be automatically sorted (small lids and pieces of cardboard/paper smaller than a credit card, for example).
So if you do put them in the recycling, youâre sending them to landfill anyway.
I found similar statements on various other state/territory government/council websites. Unfortunately, I also found many such entities that provide a recycling calendar / what-goes-where info sheet with fridge magnet attached. 
I saw this statement on one of those, https://cdn.canning.wa.gov.au/media/5w0nzbrp/waste-guide-2024.pdf
Remove magnet before placing this guide in the recycling bin.
Reuse the magnet or place in the general waste bin.
I donât think I saw the petition below when it was (presumably) circulated in 2021, but I wouldâve signed it if I had. Mind you, nothing has come of it yet.
Petition EN3208 - Ban mass distribution of Fridge Magnets | aph.gov.au
Petition Reason
The delivery of fridge magnets via Australia Post mass mail outs (or hand delivery) is environmental vandalism as the vast majority end up in landfill, without ever being used. On average, our household receives 1-2 per week, nearly every week of the year. At 10g each (assuming only 1 per week) that is 1/2 kilo of plastic/magnetic waste our household adds to landfill every year! With 40 households in our street we are contributing 20kg per year or, as a nation of over 8 million households, this equates to over 4 million KGs per year in Australia alone! The production process is also unsustainable as Magnets are made from non-renewable rare-earth metals which are mined causing significant destruction and degradation of natural ecosystems. Even if companies are using recycled materials the energy and resources used to create an item that generally is thrown straight into landfill is irresponsible and completely unnecessary.
Petition Request
We therefore ask the House to make the mass distribution of Fridge Magnets illegal as the vast majority end up in landfill and are an unnecessary burden on our fragile environment.