The cabinet considered an urgent report on Tuesday and voted to remove the section from the pavilion to the seaward end.
The report said because of the risk of further collapse, the council could not wait for consent to begin work, as is usually the case for a listed building.
Work on the "dangerous" structure is expected to take about three weeks.
Parts of the Grade ll pier, which was already closed to the public when it gave way on 1 February, will be saved, catalogued and stored.
Iwan Davies, chief executive of the council, told the meeting: "The dangerous nature of the structure means dismantling it is dangerous."
Up to Â£650,000 has been set aside for the work but councillors were told there was no way of knowing how much it would cost.
Part of Colwyn Bay pier is to be dismantled after it collapsed into the sea, Conwy council has decided.