A futon does not fit in a normal trash bag, and stuffing one in anyway is how it ends up back on the curb with a warning sticker. In most wards a futon counts as sodai gomi (粗大ごみ), oversized garbage, and oversized garbage has its own pickup process that you book ahead of time.
It sounds like a hassle the first time. It is really just four steps.
Every ward runs an oversized garbage center (粗大ごみ受付センター). You reserve a slot by phone or, in most cities now, through an online form. Tell them you have one futon. They give you a collection date and a fee. A futon usually runs somewhere around 300 to 500 yen, though the exact amount depends on your ward.
You pay by buying a sodai gomi sticker (粗大ごみ処理券) at a convenience store or supermarket. Ask the staff if you cannot find them. You buy stickers that add up to the fee you were quoted.
Write your name or the reservation number they gave you on the sticker, then stick it somewhere visible on the futon. This is how the crew knows it has been paid for and is meant to go.
Set the futon out at the spot they told you, by the morning of your collection date. Not the night before in most places, and not with the regular bags. Then it is gone.
Buying a new futon? Many retailers will take your old one when they deliver the new one, sometimes for free. Worth asking before you book a separate pickup.
The genuinely confusing part is usually the phone call and knowing what fee to expect. That is the exact moment Gomi Guide is built for.
Let Gomi Guide handle the sodai gomi call Snap the item, set your region, and the app walks you through the fee, the sticker, and what to say. Free on the App Store.