Yes, with no additional fee, but you must fold your bicycle and put it into a bicycle bag.
Tokyo Monorail’s official website says:
自転車はそのまま車内に持ち込むことはできません。
持ち込む場合には、自転車を解体、もしくは折りたたみ、専用の袋(輪行袋)に収納した上でご乗車ください。
Translation:
You can not enter the train with a bicycle as-is.
If you want to bring it, you must disassemble the bicycle (front wheel, or fold it if it is a foldable bicycle) and put it into a bicycle bag made for that purpose, then enter the train.
Article about this bag, in Japanese: https://ja.wikipedia.org/wiki/輪行袋
If you had your bicycle when landing at Haneda, chances are you have such a bag already. Otherwise, you can buy one for between 1300 and 10,000 yen.
Credit:stackoverflow.com‘
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