He becomes the second member to resign in recent weeks, after the island’s most senior politician Nigel Vooght stood down in the middle of December blaming political infighting.
It all means a by-election on Saturday 8 March.
Mr Woodhead finished bottom of the poll at the start of December in a bid to secure a seat to be the island’s representative in the States of Guernsey.
It has been a busy time for Alderney voters, who had already been to the polls to elect half of their 12 member States on 16 November and their President on 30 November.
Mr Woodhead was elected for a four year term in December 2022.
That had followed a general election on 16 November.