Treated and untreated wood go to a landfill transfer station. Do not burn treated wood. You can also check with your waste hauler to see if they will pick up small amounts of treated wood.
Call first for a Minneapolis voucher or non-resident fees. More information is available through the Minneapolis Voucher Program.
Consider alternatives to treated wood for your next outdoor project. Ask your lumberyard or home repair retailer for non-toxic treated wood options.